Issue 4 Volume 5 (2017)

Authors : Pawan Kumar and Z.K.Ansari
Title : Some Common Fixed Point Theorems of Contractive Mappings in Cone b-metric Spaces
Volume, Issue, Year : 5(4−A)(2017)
Pages : 1−8

Abstract: In this paper, we prove some common fixed point theorems of contraction mappings in cone b-metric spaces.

Keywords: Fixed point, Cone Metric Spaces, Complete Cone Metric Spaces, Cone b-Metric Spaces.

Authors : Deveneder Kumar Kamboj
Title : A Note on Extremal Disconnectedness
Volume, Issue, Year : 5(4−A)(2017)
Pages : 9−12

Abstract: In this paper, we show that in an extremally disconnected topological space, there exists a maximal family of subsets of the space containing the family of all semi-open sets, where the closure operator is distributive over the intersection of every two members of the family. A characterization of extremal disconnectedness in terms of open filters is also obtained.

Keywords: Semi-open set, extremally disconnected space, open filter, open ultrafilter.

Authors : C.D. Bele and U.P. Dolhare
Title : An Extension of Common Fixed Point Theorem in D-Metric Space
Volume, Issue, Year : 5(4−A)(2017)
Pages : 13−18

Abstract: There have been number of generalizations of Metric spaces. D--Metric space is one such generalization initiated by Dhage \cite{1} in 1984 and open new research area. Then many authors have obtained interesting fixed point results in D--Metric space satisfying contractive type condition. In this paper we proved some fixed point theorems in D--Metric space and also proved new fixed point theorem D--Metric space for a contractive self--maps.

Keywords: D--Metric space, fixed point theorems.

Authors : S. Pious Missier, C. Reena and G. Mahadevan
Title : Contra Semi*$\delta$-Continuous Functions in Topological Spaces
Volume, Issue, Year : 5(4−A)(2017)
Pages : 19−30

Abstract: In this paper we define contra-semi*$\delta$-continuous, contra-semi*$\delta$-irresolute, semi*$\delta$-open and semi*$\delta$-closed functions and investigate their properties.

Keywords: Contra-semi*$\delta$-continuous, contra-semi*$\delta$-irresolute, semi*$\delta$-open map, semi*$\delta$-closed map.

Authors : Wei-Kai Lai
Title : On a Simple Inequality Problem
Volume, Issue, Year : 5(4−A)(2017)
Pages : 31−33

Abstract: This note introduces five different proofs of a simple inequality problem applying five well-known inequalities.

Keywords: AM-GM Inequality, Radon's Inequality, Rearrangement Inequality.

Authors : U. Sharma and K. Sharma
Title : Domination Number and Total Domination Number of Square of Normal Product of Cycles
Volume, Issue, Year : 5(4−A)(2017)
Pages : 35−44

Abstract: In 1958-Claude Berge introduced the domination number of a graph which is utilized to secure the single vertices. A set $S\subseteq V(G)$ is a dominating set of $G$ if every vertex of $V(G)-S$ is adjacent to at least one vertex of $S$. The cardinality of the smallest dominating set of $G$ is called the domination number of $G$. A dominating set $S$ is called total dominating set if the induced subgraph $\langle S\rangle$ has no isolated vertex. The square $G^2$ of a graph $G$ is obtained from $G$ by adding new edges between every two vertices having distance $2$ in $G$. In this paper, we determine the domination number and total domination number of square of normal product of cycle graphs by evaluating their minimum dominating set and minimum total dominating set and short display are also provided to understand the results.

Keywords: Domination Number, Total Domination Number, Cycles, Square of a Graph, Normal Product.

Authors : S. Pinelas, M.Arunkumar and E. Sathya
Title : Hyers Type Stability of a Radical Reciprocal Quadratic Functional Equation Originating From 3 Dimensional Pythagorean Means
Volume, Issue, Year : 5(4−A)(2017)
Pages : 45−52

Abstract: In this paper, authors introduce a 3 dimensional Pythagorean mean functional equation \begin{align*} f\left(\sqrt{x^2+y^2}\right)+f\left(\sqrt{y^2+z^2}\right)+f\left(\sqrt{z^2+x^2}\right) =\frac{f(x)f(y)}{f(x)+f(y)}+\frac{f(y)f(z)}{f(y)+f(z)}+\frac{f(z)f(x)}{f(z)+f(x)} \end{align*} which relates the three classical Pythagorean mean and investigate its generalized Hyers-Ulam stability.

Keywords: Pythagorean Means, Arithmetic mean, Geometric mean and Harmonic mean, Generalized Hyers-Ulam stability.

Authors : T. Kavitha
Title : On Mildly B-Normal Spaces and Some Functions
Volume, Issue, Year : 5(4−A)(2017)
Pages : 53−60

Abstract: In this paper, by using Bg-closed sets we obtain a characterization of mildly B-normal spaces and use it to improve the preservation theorems of mildly B-normal spaces.

Keywords: Bg-closed sets, characterization of mildly B-normal spaces, mildly B-normal spaces.

Authors : Eltiyeb Ali and Ayoub Elshokry
Title : On Strongly Symmetric Rings
Volume, Issue, Year : 5(4−A)(2017)
Pages : 61−65

Abstract: A ring $R$ is called strongly symmetric, if whenever polynomials $f(x), g(x), h(x)$ in $R[x]$ satisfy $f(x)g(x)h(x) = 0,$ then $f(x)h(x)g(x) = 0.$ It is proved that a ring $R$ is strongly symmetric if and only if its polynomial ring $R[x]$ is strongly symmetric if and only if its Laurent polynomial ring $R[x, x^{-1}]$ is strongly symmetric. We also show that for a right Ore ring $R$ with $Q$ its classical right quotient ring, $R$ is strongly symmetric if and only if $Q$ is strongly symmetric. Finally we proved that, let $R$ be an algebra over a commutative ring $S,$ and $D$ be the Dorroh extension of $R$ by $S.$ If $R$ is strongly symmetric and $S$ is a domain, then $D$ is strongly symmetric.

Keywords: Reduced rings, symmetric rings, strongly symmetric rings.

Authors : Rohtash
Title : A Study on the Algorithms for Equilibrium Problems on Hadamard Manifolds
Volume, Issue, Year : 5(4−A)(2017)
Pages : 67−79

Abstract: The theory of equilibrium problems provides a unified, natural and general framework to study a wide class of problems, which arise in finance, economics, network analysis, transportation and optimization. This theory has applications across all disciplines of pure and applied sciences. Equilibrium problems include variational inequalities and related problems. The aim of this paper is to provide a survey on the algorithms for equilibrium problems that have been studied by many authors on Hadamard manifolds. This paper should be a useful reference for further research in the field of equilibrium problems and Hadamard manifolds.

Keywords: Equilibrium problems, Mixed equilibrium problems, auxiliary principle technique, Hadamard manifold.

Authors : M.S. Siddesha, C.S. Bagewadi, D. Nirmala and N. Srikantha
Title : On the Geometry of Pseudo-slant Submanifolds of LP-Cosymplectic Manifold
Volume, Issue, Year : 5(4−A)(2017)
Pages : 81−87

Abstract: In this paper, we study pseudo-slant submanifolds of LP-cosymplectic manifold and obtained some interesting characterization results.

Keywords: Slant submanifold, pseudo-slant submanifold and LP-cosymplectic manifold.

Authors : M. Sankara Narayanan, M. Menaka and M. Marudai
Title : Common Fixed Point of Three Contractive Type Mappings
Volume, Issue, Year : 5(4−A)(2017)
Pages : 89−94

Abstract: In this paper we prove common fixed point theorems for sequentially convergent Kannan and Chatterjea type mappings, which are generalization of many common fixed point theorems.

Keywords: Fixed point, Affine, Sequentially convergent, Compact.

Authors : Mallikarjuna Kumbar et al.
Title : Geometric Approach for Banach Space Using Hausdorff Distance
Volume, Issue, Year : 5(4−A)(2017)
Pages : 95−102

Abstract: In this paper, we study the normed linear spaces which are induced by Hausdorff distance. Barich proved the completeness of Hausdorff metric space \cite{c5}. We extend his work for the completeness of the normed linear spaces called Banach spaces, which are induced by Hausdorff distance and we proved convex Hausdorff metric space is Banach space.

Keywords: Convex set, Banach Space, Hausdorff Distance, Hausdorff Metric Space.

Authors : Shyam Kishor, Pushpendra Verma and Puneet Kumar Gupt
Title : On $W_{9}-$Curvature Tensor of Generalized Sasakian-Space-Forms
Volume, Issue, Year : 5(4−A)(2017)
Pages : 103−112

Abstract: The object of the present paper is to study generalized Sasakian-space-forms satisfying certain curvature conditions on $W_{9}-$ curvature tensor. In this paper, we study $W_{9}-$ semisymmetric, $W_{9}-$flat, $\xi -W_{9}-$ flat, generalized Sasakian-space-forms satisfying $I(\xi ,X).S=0,$ $I(\xi ,X).R=0,$ $I(\xi ,X).P=0$ and $I(\xi ,X).\widetilde{C}=0.$

Keywords: Generalized Sasakian-space form, $W_{9}-$ curvature tensor, Concircular curvature tensor, Ricci tensor, $\eta -$Einstein Manifold, scalar curvature.

Authors : N. Revathi and K. Bageerathi
Title : New Separation Axioms in Soft Bitopological Space
Volume, Issue, Year : 5(4−A)(2017)
Pages : 113−120

Abstract: The present paper introduces a new class of separation axioms called $(1,2)^*$-soft b-separation axioms using $(1,2)^*$-soft b-open set. Also the properties of $(1,2)^*$-soft bT$_{i}$-spaces (i =0,1,2) are soft bitopological properties under the bijection and irresolute open soft mapping. Further, we show that the properties of $(1,2)^*$-soft bT$_{i}$-spaces (i =0,1,2) are hereditary properties.

Keywords: Separation Axioms, $(1,2)^*$-soft bT$_{i}$-spaces (i =0,1,2).