Volume 5 (2017) Article in Press

ISSUE 1 − A
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Article Type : Research Article
Title : Common Fixed Point Theorem In Rational Inequality And Their Application
Country : India
Authors : Madhu Shrivastava, K.Qureshi and A.D.Singh

Abstract: In this paper we prove some sufficient condition for the existence and uniqueness of fixed point and common fixed point in rational inequality on complete metric spaces. As application, Some existence and uniqueness results of solution and common solution for some functional equations and system of functional equations in Dynamic programming are given by using the fixed point and common fixed point theorems.

Keywords: Common fixed point, complete metric space, common solution, functional equation, system of functional equations, dynamic programming.

Madhu Shrivastava
Department of Mathematics, TIT Group of Institution, Bhopal, India.
E-mail:


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Article Type : Research Article
Title : Analysis of $M^{X}/G/1$ Queueing System With Setup and Feedback Under Multiple Adapted Vacation Policy
Country : India
Authors : S.Nithya Rubini and M.I.Afthab Begum

Abstract: $M^{X}/G/1$ queueing model under server breakdown and server vacation is considered. In this model, it is assumed that, whenever breakdowns occur the server is sent for repair immediately and the service interrupted customers join the head of the queue and repeat a new service as soon as the server is fixed. The server adopts both types of vacation policy. Whenever the server completes a service, he may continue to serve the next customer with probability $\textbf{(1-p)}$ (or) take a single vacation with probability p. At the end of the vacation, the server serves the next customer. The process continues until the system becomes empty. Once the system becomes empty, the server adopts Multiple Adapted Vacation (MAV) policy which is determined by a set of probabilities. It is also assumed that the system requires a setup operation to start a new busy period. Thus the idle vacation period, setup period, busy period, breakdown period and vacation time between two consecutive services during busy period constitute a cycle.

Keywords: Batch arrival, server breakdown, feedback, MAV policy.

S.Nithya Rubini
Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Tamilnadu, India.
E-mail: @mail.com


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Article Type : Research Article
Title : Performance Analysis Of Two Echelon Perishable Inventory System With Joint Ordering Policy
Country : India
Authors : R.Karthikeyan and K.Krishnan

Abstract: Perishable inventory system has received increasing attentions in the past years. An optimal ordering policy for deteriorating inventory system has become more and more important. This paper develops a model to determine the optimal order quantity that minimizes the total expected cost for perishable items. In addition, the solution methodologies as well as an analysis of results are presented. In this study, we create a scenario where two types of products are considered with two locations (Distributor and Retailer) in such a way that there exists a joint ordering policy. A continuous review perishable inventory model with independent Poisson demand for items at retailer and a direct Poisson demand at distributor is assumed. The items are supplied to the retailers from the distribution center (DC) administrated with exponential lead time. The joint probability disruption of the inventory levels of two products at retailer and the supplier are obtained in the steady state case. Various system performance measures are derived and the long run total expected inventory cost rate is calculated. Several instances of numerical examples, which provide insight into the behavior of the system, are presented.

Keywords: Perishable inventory, Two-echelon, Joint ordering policy, Optimization.

K.Krishnan
PG\& Research Department of Mathematics, Cardamom Planters' Association College, Bodinayakanur, Tamil Nadu, India.
E-mail: drkkmaths@gmail.com


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Article Type : Research Article
Title : Some Properties of Semi ${}^{\# }$generalized Open Sets in Topological Spaces
Country : India
Authors : S.Saranya and K.Bageerathi

Abstract: In this paper a new class of generalized open sets in topological spaces, namely semi ${}^{\# }$generalized open(briefly, s${}^{\#}$g-open) sets is introduced. We prove that this class lies between the class of sg-open sets and the class of gs-open sets and we study some basic properties and characterizations of s${}^{\#}$g-open sets. Also we introduce s${}^{\#}$g-neighbourhood (shortly, s${}^{\#}$-nbhd), s${}^{\#}$g-interior, s${}^{\#}$g-closure and s${}^{\#}$g-derived set of a set in a topological spaces and investigate some basic properties of these sets.

Keywords: s${}^{\#}$g-open set, s${}^{\#}$g-neighbourhood, s${}^{\#}$g-closure, s${}^{\#}$g-interior, s${}^{\#}$g-derived set.

S.Saranya
Department of mathematics, Aditanar college of Arts and science, Tiruchendur, Tamil Nadu, India.
E-mail: saranya7873@gmail.com


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Article Type : Research Article
Title : Numerical Solution of Intuitionistic Fuzzy Differential Equation by Milne's Predictor - Corrector Method Under Generalised Differentiability
Country : India
Authors : V.Parimala, P.Rajarajeswari and V.Nirmala

Abstract: Nowadays many real life problems are identified with Fuzzy set theory. The Fuzzy set theory is a useful tool to describe the situation in which data are imprecise or vague or uncertain. This set theory is completely described by its membership function. A membership function of a classical fuzzy set assigns to each element of the universe of discourse a number from the interval $[0, 1]$ to indicate the degree of belongingness to the set under consideration. The degree of non belongingness is just automatically the complement to \ "1" of the membership degree. But many times, a human being does not express the degree of non membership as the complement to \ "1".There may be some hesitation about the belongingness and non-belongingness. This missing data or hesitation is accomplished by a set known as intuitionistic fuzzy set. In this paper, Milne's Predictor - Corrector method is used for finding numerical solution of an intuitionistic fuzzy differential equation (IFDE). The proposed method is based on the concept of generalized differentiability. IFDE is transformed into four ordinary differential systems and then Milne's Predictor - Corrector method is applied.Also,the convergence and stability of the proposed method is given and its applicability is illustrated by solving a first order IFDE.

Keywords: Intuitionistic fuzzy differential equation, Numerical methods, Milne's Predictor - Corrector, Generalised differentiability.

V.Nirmala
Department of Mathematics, University College of Engineering Tindivanam, Tamil Nadu, India.
E-mail: nirmalaucet@mail.com


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Article Type : Research Article
Title : A Note on Construction of Finite Field of Order $p$ and $p^2$
Country : India
Authors : S.K.Pandey

Abstract: In this note we construct finite field of order $p$ (here $p$ is a positive prime) and $p^{2}$ for $p>2$ through even square elements of $Z_{2p} $. It has been already noticed that a finite field of order $p^{2} $, $p>2$ can be directly constructed without using the concept of quotient rings. We utilize the same technique to yield a finite field of order $p^{2} $ for $p>2$ however here we use the notion of even square elements of a ring $R$. It is noticed that for all the finite fields constructed in this article the reducing modulo $m$ is a composite integer.

Keywords: Finite field, matrix field, matrix, even square element.

S.K.Pandey
Department of Mathematics, Sardar Patel University of Police, Security and Criminal Justice, Daijar, Jodhpur, Rajasthan, India.
E-mail: skpandey12@gmail.com


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Article Type : Research Article
Title : Some Euler Spaces of Difference Sequences and Matrix Mappings
Country : India
Authors : Shadab Ahmad Khan and Ashfaque A.Ansari

Abstract: Altay and Ba\c{s}ar [2] and Altay, Ba\c{s}ar and Mursaleen [3] introduced the Euler sequence spaces $e^r_{0\ ,}{\ e}^r_{c\ ,\ \ }\ and\ e^r_{\infty \ ,}$ respectively. Polat and Ba\c{s}ar [25] introduced the spaces $e^r_0$(${\Delta }^{(m)}$), $e^r_{c\ \ }$(${\Delta }^{(m)}$), and $e^r_{\infty \ }$(${\Delta }^{(m)}$) consisting of all sequences whose $m^{th}$ order differences are in the Euler spaces $e^r_{0,}\ e^r_{c\ ,\ \ }and\ e^r_{\infty \ ,}$ respectively. Moreover, the authors give some topological properties and inclusion relations, and determine the $\alpha$-, $\beta$-, $\gamma$-, and continuous duals of the spaces $e^r_0\ ,$ $e^r_{c\ \ },e^r_p,$ $e^r_{\infty \ },$ $e^r_0$(${\Delta }^{(m)}$), $e^r_{c\ \ }$(${\Delta }^{(m)}$) and $e^r_{\infty \ }$(${\Delta }^{(m)}$), for $1\le p<\infty $ and their basis have been constructed. The last section of the article is devoted to the characterization of some matrix mappings on the sequence spaces $e^r_{c\ \ }\ $and $e^r_{c\ \ }\mathrm{(}{\Delta }^{(m)}\mathrm{)\ }$.

Keywords: The $\alpha$-, $\beta$-, $\gamma$-, and continuous duals, basis, matrix mappings and difference sequence spaces of order m.

Shadab Ahmad Khan
Department of Mathematics & Statistics, D. D. U. Gorakhpur University, Gorakhpur, India.
E-mail: sakhanan15@gmail.com


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Article Type : Research Article
Title : Edge-Wiener Indices of $n$-Circumscribed Peri-condensed Benzenoid Graphs
Country : India
Authors : Jasintha Quadras, K.Arputha Christy and A.Nelson

Abstract: The cut method demonstrates its usefulness especially for the topological indices that are based on the distances in the molecular graphs without actually calculating the distances between pairs of vertices. The Wiener index is equal to the sum of distances between all pairs of vertices of the connected graph $G$, whereas the Edge-Wiener index is the sum of distances between all pairs of edges of the connected graph $G$. In this paper we calculate the Edge-Wiener indices of Circum-polyacenes, Circum-pyrenes and Circum-trizenes.

Keywords: Edge-Wiener indices, Cut method, Circum-polyacenes, Circum-pyrenes and Circum-trizenes.

K.Arputha Christy
Department of Mathematics, Stella Maris College, Chennai, India.
E-mail: christy.kichi@gmail.com


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Article Type : Research Article
Title : Heronian Mean Labeling of Double Triangular and Double Quadrilateral Snake Graphs
Country : India
Authors : S.S.Sandhya, E.Ebin Raja Merly and S.D.Deepa

Abstract: In this paper, We contribute some new results for Heronian Mean labeling of graphs. We prove that Double Triangular snake, Alternate Double Triangular snake, Double Quadrilateral Snake and Alternate Double Quadrilateral Snake graphs are Heronian mean graphs.

Keywords: Heronian Mean labeling, Triangular snake, Double Triangular snake, Quadrilateral snake, Double Quadrilateral Snake.

S.D.Deepa
Department of Mathematics, Nesamony Memorial Christian College, Marthandam, Tamilnadu, India.
E-mail: christodeepadit@gmail.com


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Article Type : Research Article
Title : Attractivity Result For Second Order Random Differential Equation
Country : India
Authors : P.R.Shinde and D.S.Palimkar

Abstract: In this paper, the existence and attractivity results are proved for nonlinear second order ordinary random differential equations by random version of Schauderís fixed point theorem.

Keywords: Random differential equation, multi-valued function, local attractivity ,global attractivity.

D.S.Palimkar
Department of Mathematics, Vasantrao Naik College, Nanded (M.S.), India.
E-mail: dspalimkar@rediffmail.com


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