## Volume 5 (2017)Article in Press

ISSUE 4 − A ISSUE 4 − B ISSUE 4 − C ISSUE 4 − D ISSUE 4 − E
 Authors : B.C. Dhage, N.S. Jadhav, J.N. Salunke and A.Y. Shete Title : Dhage Iteration Method for Nonlinear First Order Hybrid Functional Differential Equations of Second Type Linear Perturbations Volume, Issue, Year : 5(4−E)(2017) Pages : 605−614

Abstract: In this paper we prove the existence and approximation result for a first order nonlinear initial value problem of hybrid functional differential equations via construction of an algorithm. The main results rely on the Dhage iteration method embodied in a recent hybrid fixed point principle of Dhage (2014). An example is also furnished to illustrate the hypotheses and the abstract result of this paper.

Keywords: Hybrid functional differential equation, Dhage iteration method, Existence and Approximation theorem.

 Authors : B.C. Dhage, A.D. Kadam, J.N. Salunke and A.Y. Shete Title : On Some Fixed Point Theorems for Generalized Contractive Mappings in an Euclidean Space $\mathbb{R}^n$ Volume, Issue, Year : 5(4−E)(2017) Pages : 615−618

Abstract: In this paper a couple of fixed point theorems for contraction and Kannan mappings are proved in an Euclidean space $\mathbb{R}^n$ via calculus method and using the max/mini principle. It is shown that though our approach to Banach and Kannan mappings is different from the constructive one, we are not far away from the usual method. Actually one can take an arbitrary point $x_0\in \mathbb{R}^n$ and can define a sequence $\{x_n\}$ of iterates of the mapping under consideration. Then it is shown that the sequence converges to a fixed point geometrically.

Keywords: Contraction map, Fixed point theorem, max/mini principle.

 Authors : K.P.R. Sastry, K.K.M. Sarma, P. Krishna Kumari and Sunitha Choudari Title : Fixed Point Theorems for $\psi$-contractions in S-metric Spaces and KKS-metric Spaces Volume, Issue, Year : 5(4−E)(2017) Pages : 619−632

Abstract: In this paper we introduce the notion of $\psi$-contractions for self maps on S-metric spaces and establish a fixed point theorem for such maps. We also introduce a new subclass of S-metric spaces called KKS metric spaces and prove a fixed point theorem for a $\psi$-contraction on a KKS metric space. An open problem is also given at the end of the paper.

Keywords: S-metric space, KKS metric space, $\psi$-contraction.

 Authors : M.V. Subba Rao, M.N.R. Chowdary and J. Vijayasekhar Title : Two-person Zero-sum Game Problem Solution: Integer Simplex Method Volume, Issue, Year : 5(4−E)(2017) Pages : 633−635

Abstract: In this paper, we have calculated the optimal strategies of two-person zero-sum game problems which does not have a saddle point using Integer simplex method (Gomory's cutting plane method).

Keywords: Linear programming problem (LPP), Game problem, optimal strategies, Integer simplex method (Gomory's cutting plane method).

 Authors : Surajit Dutta Title : A New Construction of Apollonius Circle and a New Proof of Secant-Tangent Theorem Volume, Issue, Year : 5(4−E)(2017) Pages : 637−639

Abstract: Here in this paper we give an easy and elegant construction of Apollonius circle by using a simple property of isosceles triangles. We also give a simple proof of the Secant-Tangent theorem by using the same property of isosceles triangles.

Keywords: Apollonius Circle, Secant-Tangent Theorem.

 Authors : G.C. Basavaraju, M. Vishukumar and P. Raghunath Title : Metro Domination of Square Cycle Volume, Issue, Year : 5(4−E)(2017) Pages : 641−645

Abstract: Let $G=(V,E)$ be a graph.A set $S\subseteq V$ is called resolving set if for every $u,v\in V$ there exist $w\in V$, such that $d(u,w)\neq d(v,w)$. The resolving set with minimum cardinality is called metric basis and its cardinality is called metric dimention and it is denoted by $\beta (G)$. A set $D\subseteq V$ is called dominating set if every vertex not in $D$ is adjacent to at least one vertex in $D$. The dominating set with minimum cardinality is called domination number of $G$ and it is denoted by $\gamma (G)$. A set which is both resolving set as well as dominating set is called metro dominating set. The minimum cardinality of a metro dominating set is called metro domination number of $G$ and it is denoted by $\gamma_ \beta(G)$. In this paper we determine metro domination number of square cycle.

Keywords: Power graph, metric dimension, landmark, distance matrix.

 Authors : Amar Nath and Manohar Singh Chahar Title : Study and Analysis of Almost Para Sasakian Type-Riemannian Manifold Volume, Issue, Year : 5(4−E)(2017) Pages : 647−654

Abstract: In this paper, author studied and analyses Almost Para Sasakian Type-Riemannian manifold. The first section of this paper is introductory in nature, which deals with basic definition and literature review with previous known defined results. Second section deals with Almost Para Sasakian Type-Riemannian manifold (APST-Riemannian manifold) and its various applications and the third section is devoted for Para-K-contact type Riemannian manifold (PKCT-Riemannian manifold). As the outcomes of this work further detail theorems are suggested for future work.

Keywords: APST-Riemannian manifold, PQST manifold, PKCT-Riemannian manifold, tensor analysis, differential geometry.

 Authors : N.B. Rathod and K.K. Kanani Title : $k$-cordial Labeling of Triangular Belt, Alternate Triangular Belt, Braid Graph and $Z$-$P_n$ Volume, Issue, Year : 5(4−E)(2017) Pages : 655−662

Abstract: In this research paper, we find $k$-cordial labeling of some special graphs. We prove that Triangular Belt $TB(n)$$(\downarrow^n), Alternate Triangular Belt ATB(n)$$(\downarrow\uparrow\downarrow\uparrow...)$ and Braid Graph $B(n)$ are $k$-cordial. Moreover, the graph $Z$-$P_{n}$ is $k$-cordial for all odd $k$.

Keywords: Abelian Group, $k$-cordial Labeling, Triangular Belt, Alternate Triangular Belt, Braid graph, $Z$-$P_{n}$.

 Authors : V.R.Kulli Title : Revan Indices of Oxide and Honeycomb Networks Volume, Issue, Year : 5(4−E)(2017) Pages : 663−667

Abstract: There are many types of topological indices. Among degree based topological indices, Zagreb indices, Banhatti indices, Gourava indices are studied well. In this paper, we introduce the Revan indices and compute exact formulas for oxide and honeycomb networks.

Keywords: Revan indices, molecular graph, oxide network, honeycomb network.

 Authors : Hongyan Guan and Yan Hao Title : Products of Toeplitz and Hankel Operators on the Harmonic Bergman Space Volume, Issue, Year : 5(4−E)(2017) Pages : 669−673

Abstract: In this paper, we discuss the product problems of Toeplitz operators, small Hankel and big Hankel operators with quasihomogeneous symbols on the harmonic Bergman space of the unit disk.

Keywords: Toeplitz operator, small Hankel operator, big Hankel operator, quasihomogeneous symbols, harmonic Bergman space.

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