Volume 6 (2018) Article in Press

Authors : K. Selva Rani, M. Himaya Jaleela Begum and S. Syed Ali Fathima
Title : On Contra Weakly $\mu g$-Continuous Function in Generalized Topological Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 1−5

Abstract: In this paper we introduce some new class of functions called contra w$\mu$g-continuous functions and contra w$\mu$g-irresolute functions using w$\mu$g-closed sets in generalized topological space. We investigate their relationships with other existing functions in generalized topological space. Also we prove that composition of two contra w$\mu$g-continuous need not be contra w$\mu$g-continuous.

Keywords: w$\mu$g-closed sets, contra w$\mu$g-continuous functions, contra w$\mu$g-irresolute functions.

Authors : S. Rohini and S. Syed Ali Fathima
Title : On Soft $g^{**} \mu$-Closed Sets in Soft Generalized Topological Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 7−12

Abstract: In this paper we introduce some new class of sets called soft $g\mu$-closed sets,soft $g^{*}\mu$-closed sets and soft $g^{**} \mu$-closed sets in soft generalized topological spaces and some of their properties are established.Further, by using soft $g^{**} \mu$-closed sets we introduce soft $T_{\mu_{g^{**}}}$-space.

Keywords: Soft $g\mu$-closed sets, soft $g^{*}\mu$-closed sets, soft $g^{**} \mu$-closed sets and soft $T_{\mu_{g^{**}}}$-space.

Authors : M. Janaki, K. Kanagarajan and D. Vivek
Title : Existence Results for Katugampola-type Fractional Functional Differential Equations
Volume, Issue, Year : 6(2−A)(2018)
Pages : 13−20

Abstract: In this paper, the initial value problem is discussed for a class of Katugampola-type fractional functional differential equations and the criteria on existence are obtained.

Keywords: Katugampola fractional derivative, Fractional functional differential equations, Fractional neutral functional differential equations, Existence, Fixed point.

Authors : D. Vivek, K. Kanagarajan and S. Harikrishnan
Title : Analytic Study on Nonlocal Initial Value Problems for Pantograph Equations with Hilfer-Hadamard Fractional Derivative
Volume, Issue, Year : 6(2−A)(2018)
Pages : 21−32

Abstract: This paper is concerned with the existence and stability of solutions for a new class of nonlocal initial value problems involving Hilfer-Hadamrad type fractional pantograph equations. The existence results are obtained with the aid of some classical fixed point theorems, while the uniqueness of solutions is established by means of classical contraction mapping principle. We also discuss Ulam-Hyers stability for proposed problem.

Keywords: Fractional pantograph equations, Hilfer fractional derivative, Existence, Fixed point, Ulam stability.

Authors : Vadivel Sadhasivam, Nagamanickam Nagajothi and Muthusamy Deepa
Title : Oscillation of Fractional Nonlinear Partial Differential Equations with Continuous Distributed Deviating Arguments
Volume, Issue, Year : 6(2−A)(2018)
Pages : 33−42

Abstract: In this article, we establish some oscillation criteria for the fractional order partial differential equation with continuous distributed deviating arguments of the form \begin{align*} \dfrac{\partial}{\partial t}\left[r(t)D_{+,t}^{\alpha}\left(u(x,t)-\int_{\gamma}^{\delta}{q_0}(t,\zeta)u(x,\rho(t,\zeta))d\eta(\zeta)\right)\right]&=a(t)\Delta u(x,t)+\int_{c}^{d}p(t,\xi)\Delta u[x,\tau(t,\xi)]d\omega(\xi)\\ -\int_{c}^{d}q(x,t,\xi)g\left(u[x,\sigma(t,\xi)]\right)d\omega(\xi)+f(x,t),~~(x,t)\in G&=\Omega\times \mathbb{R}_+, \end{align*} with subject to the boundary conditions \begin{align*} \dfrac{\partial u(x,t)}{\partial \nu}+\mu(x,t) u(x,t)=\psi(x,t), \hspace{0.15in} (x,t)\in\partial\Omega \times \mathbb{R}_{+} \end{align*} and $u=\chi(x,t)$, $(x,t)\in\partial\Omega\times \mathbb{R}_{+}$. Using the generalized Riccati technique and integral averaging method, new oscillation criteria are obtained.

Keywords: Fractional partial differential equation, continuous deviating arguments, oscillation.

Authors : D. Balraj, V. Piramanantham and A. H. Ansari
Title : Existence of Best Proximity Points for Proximal C-Contractions Satisfying Rational Expression on Ordered Metric Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 43−51

Abstract: The aim of this paper is to present in the partial order metric space setting,the concept of C-class functions has been introduced and existence of best proximity point has been proved. Our rational type mapping generalisations in both contraction mapping and also generalisations the results of Luong and Thuan \cite{e}. Moreover, some examples are given to support the main results.

Keywords: Best proximity point, fixed point, $C$-class function.

Authors : M. Janaki, K. Kanagarajan and D. Vivek
Title : Analytic Study on Fractional Implicit Differential Equations with Impulses via Katugampola Fractional Derivative
Volume, Issue, Year : 6(2−A)(2018)
Pages : 53−62

Abstract: In this paper, we establish certain conditions for the existence and uniqueness of solutions for such a class of fractional implicit differential equations using Katugampola fractional derivative in Caputo. The arguments are based on fixed point theorems. We provide an example, which shows the validity of our main results.

Keywords: Generalized fractional derivative, Fractional implicit differential equations, Impulses, Fixed point.

Authors : Handan Akyar
Title : On the Cartesian Product of Generalized Fibonacci Graphs
Volume, Issue, Year : 6(2−A)(2018)
Pages : 63−70

Abstract: In this article generalized Fibonacci graphs and their Cartesian product graphs are considered. These graph's certain fundamental properties, such as number of edges, planarity, diameter, radius, center, distance center, Wiener index, etc. are studied.

Keywords: Graph Theory, Generalized Fibonacci Graphs, Cartesian Product.

Authors : Ritika
Title : Common Fixed Points of Generalized Quasi--Contractive Type Operators By a Three-Step Iterative Process in CAT(0) Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 70−77

Abstract: The aim of this paper is to approximate common fixed points of a recent three step iterative process essentially due to Thakur et al \cite {16} for two generalized quasi--contractive type operators and establish strong convergence result for the same operators in $CAT(0)$ spaces. The results obtained in this paper extend and improve the recent ones announced by Saluja \cite {15} , Xu and Noor \cite {17}, Noor \cite {13}, Picard \cite {14}, Mann \cite {12}, Ishikawa \cite {10} and many others.

Keywords: CAT(0) spaces, Generalized Quasi--Contractive type operators, Common Fixed Points, Strong convergence.

Authors : Md. Mamun Ar Rashid
Title : Generalized Semi-closed Sets in a Space
Volume, Issue, Year : 6(2−A)(2018)
Pages : 79−82

Abstract: In this paper the concept of generalized semi-closed sets and generalized semi open sets are introduced and some of its properties are investigated in a space considered by Aiexandroff A.D. \cite{1} where arbitrary union of open sets may not be open.

Keywords: Generalised semi-closed set (g*s closed set), generalized semi open set (g*s open set).

Authors : G. V. R. Babu, P. S. Kumar and G. Satyanarayana
Title : Fixed Points of Generalized $\alpha-\beta-\psi-$Contractive Mappings in Partially Ordered Complete Metric Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 83−22

Abstract: In this paper, we introduce the notion of generalized $\alpha-\beta-\psi-$contractive mappings and provide sufficient conditions for the existence and uniqueness of a fixed points for such mappings in partially ordered metric spaces. We deduce some corollaries and provide examples in support of our main results. Our results generalize the results of Asgari and Badehian \cite{Asgari}.

Keywords: Fixed point, generalized $\alpha-\beta-\psi-$ contractive map, $\alpha-\beta-$admissible map, partially ordered complete metric space.

Authors : N. P. Muktawar and D. S. Palimkar
Title : Asymptotic Attractivity and Stability for Random Functional Differential Equation
Volume, Issue, Year : 6(2−A)(2018)
Pages : 93−98

Abstract: The random differential equations appears quite naturally in the study of changes or the rate of change of any processes like diffusion process or Brownian motion. The random differential equations have been the subject of rather extensive research area since long time. It have been utilized as models for a wide variety of random problems that have been encountered time and in the areas of all areas like Sciences and Environmental Sciences. In this paper, we have discussed an existence results for local asymptotic attractivity and asymptotic stability of random solution for nonlinear random functional differential equations in Banach algebra through hybrid random fixed point theorem. The results obtained, is generalize and extend the asymptotic attractivity and stability of random solutions for concerning random functional differential equations.

Keywords: Asymptotic attractivity, Stability, random functional differential equation, Banach algebra.

Authors : Amit Gupta, Gajendra K. Saraswat and Ravendra Singh
Title : Slip Effects on Blood Flow in the Presence of a Bell-shaped Stenosed Artery: A Casson Fluid Model
Volume, Issue, Year : 6(2−A)(2018)
Pages : 99−106

Abstract: In this a paper, one dimensional Casson fluid flow under the influence of bell shaped stenosed artery have been considered. Analytical and numerical techniques both are carried out to observe this situation. Analytical expressions for axial velocity, plug flow velocity, volumetric flow rate, pressure gradient and wall shear stress has been derived. Numerical techniques have been used to show the effects of yield stress, slip and no slip velocity on these flow variables. The results show that wall shear stress increases as the values of yield stress diminishes and increase in slip velocity reduces the wall shear stress. It is also observed that plug flow velocity increases as slip velocity increases, pressure gradient increases as the slip velocity increases whereas it reduces as yield stress diminishes and axial velocity increases as velocity slip increases.

Keywords: Casson Fluid, Yield Stress, slip velocity, plug flow velocity.

Authors : Porkodi Chinniah and Arumuganathan Ramalingam
Title : An Integer Factorization Method Equivalent to Fermat Factorization
Volume, Issue, Year : 6(2−A)(2018)
Pages : 107−111

Abstract: Integer factorization problem had a great impact on security of many public key cryptosystems. Advancement in factoring increases the need to develop innovative public key cryptosystems. In this paper, a special purpose factorization method to find the factors of a composite number, which is the product of two distinct primes, is proposed. Fermat's method is theoretically important and many modern factorization algorithms like the quadratic sieve, multiple polynomial quadratic sieve, and number field sieves are based upon this method. The proposed scheme is equivalent to Fermat's method, and hence it can be used in such popular modern factorization methods. The steps involved in the algorithm are proved theoretically. Algorithm is illustrated numerically using Mathematica.

Keywords: Integer factorization problem, Division algorithm, Fermat's method, Greatest Common Divisor.

Authors : Swarnima Bahadur and Ravindra Kumar Katheriya
Title : On (0,1,2) Trigonometric Interpolation
Volume, Issue, Year : 6(2−A)(2018)
Pages : 113−118

Abstract: The aim of this paper is to discuss the case of $(0,1,2)$ interpolation by trigonometric polynomial on the zeros of $\sin mx$ at the point $x_k$=$\frac{2\pi k}{n}$, where $k=0,1,2,\dots,n-1$, where n is even $(n=2m)$ and the convergence behavior of this trigonometric polynomial. Let $R_n(x)$ be a trigonometric polynomial of order such that \begin{align*} R_n(x_k)&=a_k\\ R'_n(x_k)&=b_k\\ R''_n(x_k)&=c_k \end{align*} where $x_k$=$\frac{2\pi k}{n}$, $k=0,1,2,\dots,n-1$ and $n$ is even $(n=2m)$.

Keywords: Trigonometric polynomial, Interpolation, Explicit representation, Estimates, Convergence.

Authors : K. Ramalakshmi and K. Palani
Title : Independent and Upper Steiner Domination Number of Graphs
Volume, Issue, Year : 6(2−A)(2018)
Pages : 119−124

Abstract: In this paper, independent and upper steiner domination number of graphs are introduced. Also, these numbers were found for some standard graphs.

Keywords: Steiner number, steiner domination number, independent steiner domination number, upper steiner domination number.

Authors : B. Prabhakar Reddy
Title : Viscous Dissipation Effects on Unsteady MHD Flow Past an Impulsively Started Infinite Isothermal Vertcal Plate in The Presence of Radiation
Volume, Issue, Year : 6(2−A)(2018)
Pages : 125−134

Abstract: In this paper, the effects of viscous dissipation on an unsteady MHD viscous incompressible fluid flow past an impulsively started infinite isothermal vertical plate in the presence of radiation has been presented. The fluid is considered gray, absorbing-emitting radiation but a non-scattering medium. Thermal radiation effects are simulated via a radiation parameter $N$, based on the Rossseland diffusion approximation. The momentum and thermal boundary layer equations are non-dimensionalized using appropriate transformations and then solved numerically subject to physically realistic boundary conditions by using the Ritz finite element method. The influence of physical parameters on the velocity profiles $(u)$, temperature distribution $(\theta )$, skin-friction $(\tau )$, and the Nusselt number $(Nu)$ are presented with the help of graphs and tables. The obtained results show that a decrease in the velocity and temperature as the radiation parameter is increased. The velocity $u$ is decreased as the magnetic parameter increases and increases with increasing Grashof number and time parameter. The skin-friction increases with increase in the magnetic parameter and decreases with increasing Grashof number and Eckert number.

Keywords: MHD, magnetic parameter, radiation parameter, isothermal vertical plate, Ritz finite element method.

Authors : Fernandes Gloria and Tabitha Agnes Mangam
Title : Isolate Domination in Total graphs
Volume, Issue, Year : 6(2−A)(2018)
Pages : 135−139

Abstract: A dominating set $S$ of a graph $G$ is said to be an isolate dominating set of $G$ if induced subgraph on $S$ has at least one isolated vertex. An isolate dominating set $S$ is said to be a minimal isolate dominating set if no proper subset of $S$ is an isolate dominating set. The isolate domination number $\gamma_0$ is defined as the minimum cardinality of minimal isolate dominating set. In this paper, we investigate the isolate domination number of total graphs of certain classes of graphs.

Keywords: Domination number, Isolate domination number, Total graph.

Authors : S. Lavanya and S. Ramya
Title : Edge Domination in Some Special Classes of Fuzzy Graphs
Volume, Issue, Year : 6(2−A)(2018)
Pages : 141−144

Abstract: In this paper we find the exact edge domination number of some special classes of fuzzy graphs like complete fuzzy graph, star fuzzy graph complete bipartite fuzzy graph etc.

Keywords: Edge domination, complete fuzzy graph, star fuzzy graph, regular fuzzy graph.

Authors : G. Ayyappan and S. Karpagam
Title : An $M^{[X]}/G(a,b)/1$ Queueing System with Breakdown and Second Optional Repair, Stand-by Server, Balking, Variant Arrival Rate and Multiple Vacation
Volume, Issue, Year : 6(2−A)(2018)
Pages : 145−156

Abstract: In this paper, we discussed a Non-Markovian batch arrival general bulk service single server queueing system with server's breakdown and second optional repair, stand-by server, balking, variant arrival rate and multiple vacation. The main server's service time, vacation time, stand-by server's service time are all follows general distributions and breakdown and two types of repair time for main server follows exponential distributions. There is a stand-by server which is employed during the period for which the regular server remains under repair. The probability generating function of queue size at an arbitrary time and some performance measures of the system are derived. Extensive numerical results are also illustrated.

Keywords: Non-Markovian queue, General bulk service, Multiple vacation, Breakdown and optional Repair, Stand-by server, Balking, Variant arrival rate.

Authors : M.M. Iddrisu
Title : q-Steffensen's Inequality for Convex Functions
Volume, Issue, Year : 6(2−A)(2018)
Pages : 157−162

Abstract: In this paper, q- Steffensen's Inequality for convex functions is presented with illustrative examples. Review of research works on Steffensen's Inequality and q-calculus is extensively carried out. Methods of q- differentiability and monotonicity of functions are employed to establish the results.

Keywords: Steffensen's Inequality, Convex functions, q-calculus.

Authors : K. Nantomah, M. M. Iddrisu and C. A. Okpoti
Title : On a $q$-analogue of the Nielsen's $\beta$-Function
Volume, Issue, Year : 6(2−A)(2018)
Pages : 163−171

Abstract: Motivated by the Jackson's $q$-integral and the $q$-digamma function, we introduce a $q$-analogue of the Nielsen's $\beta$-function. We further study some identities, monotonicity and convexity properties, and some inequalities involving the new function.

Keywords: Nielsen's $\beta$-function, Jackson's $q$-integral, $q$-digamma function, $q$-analogue, inequality.

Authors : Tresa Mary Chacko and D. Susha
Title : Binary Linear Topological Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 173−179

Abstract: In this paper we define and study the concept of binary linear topological spaces (BLTS) and their properties. Here we prove that the binary product of two linear topological spaces is a BLTS. Also we have the main result that the binary product preserve metrizability and normability. Finally we construct a BLTS from a family of binary seminorms on a pair of vector spaces.

Keywords: Linear Topological Spaces, Binary topology, locally convex, metrizable.

Authors : M. Tamilselvi and N. Revathi
Title : k-Harmonic Mean Labeling of Some Cycle Related Graphs
Volume, Issue, Year : 6(2−A)(2018)
Pages : 181−191

Abstract: Somasundaram and Ponraj \cite{12} have introduced the notion of mean labeling of graphs. R. Ponraj and D. Ramya introduced Super mean labeling of graphs in \cite{5}. S. Somasundaram and S.S. Sandhya introduced the concept of Harmonic mean labeling in \cite{6} and studied their behavior in \cite{7,8,9}. In this paper, we investigate k-harmonic mean labeling of some graphs.

Keywords: Harmonic mean labeling, harmonic mean graph, k-harmonic mean labeling, k-harmonic mean graph.

Authors : V. Rajendran, P. Sathishmohan and K. Lavanya
Title : On $\mathcal{NI}_{\widehat g}$-Closed Sets in Nano Ideal Topological Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 193−199

Abstract: This paper focuses on $\mathcal {NI}_{\widehat {g}}$-Closed sets (nano $\mathcal {I} _{\widehat {g}}$-closed sets) and $\mathcal {NI}_{\widehat {g}}$-open sets (nano $\mathcal {I} _{\widehat {g}}$-closed sets) in nano ideal topological spaces and certain properties of these are investigated. We also investigate the concept of nano $\mathcal {I} _{\widehat {g}}$-closed sets and discussed their relationships with other forms of nano ideal sets. Further, we have given an appropriate examples to understand the abstract concepts clearly.

Keywords: ${\mathcal {N}g}$-closed sets, ${\mathcal {N}}{\widehat{g}}$-closed sets, ${\mathcal {NI}}_{g}$-closed sets, ${\mathcal {NI}}_{\widehat {g}}$-closed sets and ${\mathcal {NI}}_{\widehat g}$-open sets.

Authors : P. Sathishmohan, V. Rajendran and P. Jeevitha
Title : On $\pi g^\ast$s-Irresolute Functions in Topological Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 201−207

Abstract: The purpose of this paper is to defined and studied the notion of $\pi$ generalized star semi-closed sets in topological spaces and some of their basic properties are investigated. This new class of sets lies between the class of $\pi$g-closed sets and the class of $\pi$gs-closed sets. Further the notion of $\pi g^\ast$s-open sets, $\pi g^\ast$s-continuous functions and $\pi g^\ast$s-irresolute functions are defined and the composition of two $\pi g^\ast$s-irresolute functions are discussed. Several examples are provided to illustrate the behaviour of new sets and functions.

Keywords: $\pi g^\ast$s-closed sets, $\pi g^\ast$s-open sets, $\pi g^\ast$s-continuous functions, $\pi g^\ast$s-irresolute functions.

Authors : Parajal Rai
Title : A Study on Factoriangular Numbers
Volume, Issue, Year : 6(2−A)(2018)
Pages : 209−218

Abstract: In this paper, we prove that there is no factoriangular number that is also factorial. An expression of factoriangular number explicitly in terms of triangular number is given. Bounds of the ratio of consecutive factoriangular number are given. It is shown that for n $\geq$ 5, there exists no $Ft_{n}$ which divides $Ft_{n+1}$. Patterns in factoriangular number modulo n is also observed. It is conjectuerd that there exists no factoriangular number that is a perfect square. It has also been conjectured that for n $\geq$ 6, 8n! + 1 is not a perfect square. A conjecture \cite{cas} that there is no factoriangular number that is an even perfect number is proved.

Keywords: Factoriangular Numbers, Generalized Factoriangular Numbers, even perfect number.

Authors : A. Sahaya Sudha and K. R. Vijayalakshmi
Title : Arithmetic Operations of Hexagonal Intuitionistic Fuzzy Number Using Extension Principle
Volume, Issue, Year : 6(2−A)(2018)
Pages : 219−225

Abstract: This paper presents an analysis of the basic definitions of the theory of intuitionistic fuzzy sets. Some arithmetic operations using membership and non-membership functions on Hexagonal intuitionistic fuzzy numbers are revealed and the ways to approve the properties using $(\alpha ,\beta )$ cut intervals of intuitionistic fuzzy arithmetic are proposed. The concept is illustrated with numerical example.

Keywords: Extension principle, Hexagonal intuitionistic fuzzy number, Intuitionistic fuzzy sets, $(\alpha ,\beta )$ cut intervals.

Authors : Nistala V.E.S. Murthy and Chundru Maheswari
Title : Representation of Soft Subsets by Products
Volume, Issue, Year : 6(2−A)(2018)
Pages : 227−241

Abstract: In this paper, we show that for any soft set over a universal set, 1. there is a crisp set such that the complete lattice of all soft subsets of the given soft set is complete epimorphic to a complete lattice of certain subsets of the crisp set, where the join in the later complete lattice is the meet induced join and 2. there is a crisp set such that the complete lattice of all regular soft subsets of the given soft set is complete isomorphic to a complete lattice of certain subsets of the crisp set, where the meet in the former complete lattice is the join induced meet and the join in the later complete lattice is the meet induced join.

Keywords: Factorizable subset, (Extended) Soft (sub) set, Associated product set for a soft set.

Authors : Hamant Kumar
Title : Almost $\beta$-Regular Spaces and Almost $rg\beta$-Closed Functions
Volume, Issue, Year : 6(2−A)(2018)
Pages : 243−250

Abstract: The aim of this paper is to introduce and study a new class of spaces, namely almost $\beta$-regular spaces which are generalizations of the concepts of almost regular spaces and $\beta$-regular spaces and to obtain some characterizations of almost $\beta$-regular spaces. Further, by using $rg\beta$-closed sets, we define almost $rg\beta$-closed functions and to obtain preservation theorems of almost $\beta$-regular spaces. The relationships among p-regular, $\beta$-regular, almost regular, almost p-regular, almost $\beta$-regular spaces are investigated. The main result of this paper is that almost $\beta$-regularity is preserved under M-$\beta$-open $\beta$-$rg\beta$-closed surjective R-maps.

Keywords: $\beta$-open and regular open sets, almost regular and almost $\beta$-regular spaces, $\beta$-$g\beta$-closed, $\beta$-$rg\beta$-closed, almost $\beta$-closed, almost $rg\beta$-closed and almost continuous functions.

Authors : P. Srikanth Rao and Veena Kulkarni
Title : Fixed Point Theorem for Occasionally Weakly Compatible Mappings With Common Limit Range Property Satisfying Generalized $(\psi,\phi)$-Weak Contractive Conditions
Volume, Issue, Year : 6(2−A)(2018)
Pages : 251−261

Abstract: In this paper, we prove some common fixed point theorems for occasionally weakly compatible mappings in metric spaces satisfying generalized $(\psi,\phi)$-contractive conditions under the common limit range property. We present fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. Our results improve and extend the corresponding results of Mohammad Imdad, Sunny Chauhan and ZoranKadelburg(Mathematical Sciences 7(16): 1-8, 2013).

Keywords: Metric space, Occasionally weakly compatible mappings, Property (E.A), Generalized weak contraction, Common limit range property, Common fixed point.

Authors : S. Parimala, Kalyanasundaram Madhu and Jayakumar Jayaraman
Title : Revisit of Ostrowski's Method and Two New Higher Order Methods for Solving Nonlinear Equation
Volume, Issue, Year : 6(2−A)(2018)
Pages : 263−270

Abstract: In this paper, we have obtained the Ostrowski's method in a different way and proposed two new methods of order seven and thirteen. The efficiency index of Ostrowsky's method is 1.587 and that of the seventh order method and thirteenth order method are respectively 1.626 and 1.670, which are better than Newton's method (1.414) and Ostrowsky's method. Also it is observed from the numerical illustrations, the proposed methods take less number of iterations than Newton's method. Few other methods are compared with the proposed two methods, where the number of iterations for those methods are either same or more than the presented methods. Some examples are given to illustrate the performance of the new methods.

Keywords: Non-linear equation, multi-point iteration, optimal order, Kung-Traub conjecture, higher-order method.

Authors : Manish Sharma
Title : A Fixed Point Result in Dislocated Quasi b-Metric Space
Volume, Issue, Year : 6(2−A)(2018)
Pages : 271−274

Abstract: The purpose of this paper is to consider the notion of dislocated quasi b-metric space and establish a fixed point theorem using symmetric rational type contractive condition in the context of dislocated quasi b-metric space as a generalization of Banach contraction principle.

Keywords: Dislocated quasi b-metric space, rational type contraction, fixed point.

Authors : Rafia Aziz and Rinku Verma
Title : Fixed Point Theorem for Mappings Satisfying Certain Rational Inequality
Volume, Issue, Year : 6(2−A)(2018)
Pages : 275−277

Abstract: The authors of \cite{1,2} and \cite{3} proved some fixed point theorems in complete metric space. In this paper we prove some fixed point theorems in complete metric space for mappings satisfying certain rational inequality.

Keywords: Fixed point, common fixed point, self mapping and complete metric spaces.

Authors : Ranu Sharma, Bhagyashri A. Deole and Smita Verma
Title : Some Properties of Tri-b Open Sets in Tri Topological Space
Volume, Issue, Year : 6(2−A)(2018)
Pages : 279−287

Abstract: The main aim of this paper is to study tri b-open sets in tri topological spaces along with their several properties and characterization. We study tri b-continuous, tri-b separation and obtain some of their basic properties.

Keywords: Tri topology, tri b-open sets,tri b-continuous function, tri-gb-closed, tri-b separation.

Authors : Deepak Jain
Title : Common Fixed Point Theorem for Compatible Mappings of Type (K) in Digital Metric Spaces
Volume, Issue, Year : 6(2−A)(2018)
Pages : 289−293

Abstract: In this paper, first we introduce the notion of compatible mappings of type $(K)$ in digital metric spaces analogue to the notion of compatible mappings of type $(K)$ in metric spaces and then we prove a common fixed point theorem for pairs of compatible mappings of type $(K)$ in digital metric spaces.

Keywords: Fixed point, digital image, compatible mappings of type $(K)$, digital metric space.

Authors : Manoj Kumar Sharma
Title : An Inventory Model for Deteriorating Products with Demand Appraise by Promotional Effort
Volume, Issue, Year : 6(2−A)(2018)
Pages : 295−301

Abstract: In Modern era when trends in technology, fashion and consumer change rapidly; the major problem faced by the retailer is how they can manage the deteriorating stock at time of product's self-life. In general they use some promotions efforts like price discount to prop up demand. We have tried to deal with such problem in this paper. We study the inventory problem of non-instantaneous single period deteriorating items with two parameter weibull distribution. We are considering two types of demand in this paper. First, it is function of time and then contain price factor to grown promotional effort. The holding cost is considered as constant. An approach is proposed to maximize total profit and optimal order quantity. Numerical examples illustrate the theoretical results and sensitivity analysis done as well.

Keywords: Deterministic inventory model, weibull distribution, promotional efforts, demand function.

Remaining articles will be updated soon.