## Issue 4 − AVolume 3 (2015)

ISSUE 4 − A ISSUE 4 − B ISSUE 4 − C ISSUE 4 − D ISSUE 4 − E ISSUE 4 − F
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 Article Type : Research Article Title : Integral Solutions of the Octic Equation With Five Unknowns $(x-y)(x^{3}+y^{3})=4(w^{2}-p^{2})T^{6}$ Country : India Authors : S.Vidhyalakshmi || A.Kavitha || M.A.Gopalan

Abstract: The non-homogeneous octic equation with five unknowns represented by the Diophantine equation $(x-y)(x^{3}+y^{3})=4(w^{2}-p^{2})T^{6}$ is analyzed for its patterns of non-zero distinct integral solutions and seven different patterns of integral solutions are illustrated. Various interesting relations between the solutions and special numbers, namely, Pyramidal numbers, Pronic numbers, Stella octangular numbers, Gnomonic numbers, polygonal numbers, four dimensional figurate numbers are exhibited.

Keywords: Octic non-homogeneous equation, Pyramidal numbers, Pronic numbers, Fourth, fifth and sixth dimensional figurate numbers.

M.A.Gopalan
Department of Mathematics, Shrimati Indira Gandhi College, Trichy, Tamilnadu, India.
E-mail: mayilgopalan@gmail.com

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 Article Type : Research Article Title : Oscillatory Properties of Third-Order Neutral Delay Difference Equations Country : India Authors : A.George Maria Selvam || M.Paul Loganathan || K.R.Rajkumar

Abstract: The objective of this paper is to examine oscillatory properties of the third order neutral delay difference equations of the form \begin{equation*} \Delta \left(a(n)\Delta \left(b(n)\Delta\left(x(n)+p(n)x(\sigma(n))\right)\right)\right)+q(n)x(\tau(n))=0. \end{equation*} Riccati transformation technique is used to obtain some new oscillation criteria.

Keywords: Oscillation, third order, difference equations.

A.George Maria Selvam
Department of Mathematics, Sacred Heart College,Tirupattur - 635 601, S.India.
E-mail: agmshc@gmail.com

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 Article Type : Research Article Title : On Mild Solutions of Nonlocal Semilinear Impulsive Functional Integro-Differential Equations of Second Order Country : India Authors : Rupali S. Jain || M. B. Dhakne

Abstract: This paper investigates the existence, uniqueness and continuous dependence on initial data of mild solutions of second order nonlocal semilinear functional impulsive integro-differential equations of more general type with delay in Banach spaces by using Banach contraction theorem and theory of cosine family of operators.

Keywords: Existence, uniqueness , impulsive, functional integro-differential equation, fixed point, Cosine family, second order.

Rupali S. Jain
School of Mathematical Sciences, Swami Ramanand Teerth Marathwada University, Nanded, India.
E-mail: rupalisjain@mail.com

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 Article Type : Research Article Title : Some Fixed Point Theorems under Generalized Expansion Principle with Control Function Country : India Authors : Ritu Sahu || P L Sanodia || Arvind Gupta

Abstract: We prove common fixed point theorems for semi and weak compatible mapping satisfying a generalized expansion principle by using a control function. Our theorems generalize recent results existing in the literature.

Keywords: Generalized expansion principle, Weak compatible, Semi compatible, Commute map, Control function.

Ritu Sahu
Department of Mathematics, People's College of Research & Technology, Bhopal, India.
E-mail: sahuritu00@gmail.com

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 Article Type : Research Article Title : Some Results on Soft Sequences Country : India Authors : B.S.Reddy || K.Yogesh || S.Jalil

Abstract: In this Paper, we discuss soft sequence, cluster point, limit point and convergence of soft sequence. We then prove some of the results related to these concepts.

Keywords: Soft set, Soft bounded, soft metric, soft open, soft continuous, soft Lipschitz, soft complete.

B.S.Reddy
School Of Mathematical Sciences, Swami Ramanand Tirth Marathwada University, Nanded, India.
E-mail: surendra.phd@gmail.com

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 Article Type : Research Article Title : Stability of a Quadratic Functional Equation Originating From Sum of the Medians of a Triangle in Fuzzy Ternary Banach Algebras: Direct and Fixed Point Methods Country : India Authors : John. M. Rassias || M. Arunkumar || S. Karthikeyan

Abstract: In this paper, we obtain the solution in vector space and the generalized Ulam-Hyers stability of the ternary quadratic homomorphisms and ternary quadratic derivations between fuzzy ternary Banach algebras associated to the quadratic functional equation \begin{align*} f\left(\frac{x+y}{2}-z\right)+f\left(\frac{y+z}{2}-x\right)+f\left(\frac{z+x}{2}-y\right)=\frac{3}{4}\left(f(x-y)+f(y-z)+f(z-x)\right) \end{align*} originating from sum of the medians of a triangle by using direct and fixed point methods. An application of this functional equation is also studied.

Keywords: Fuzzy ternary Banach algebra, Quadratic functional equation, Ulam - Hyers stability, Fixed point method.

M. Arunkumar
Department of Mathematics, Government Arts College, Tiruvannamalai, Tamil Nadu, India.
E-mail: annarun2002@yahoo.co.in

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 Article Type : Research Article Title : On Weakly Concircular Symmetries of Three-Dimensional ${\epsilon}-$Trans-Sasakian Manifolds Country : India Authors : Shyam Kishor || Abhishek Singh

Abstract: The object of the present paper is to study weakly concircular symmetric and weakly concircular Ricci symmetric three-dimensional $\epsilon-$ Trans-Sasakian manifolds. Futher, non existence of weakly concircular symmetric$\$and weakly concircular Ricci symmetric three dimensional $\epsilon-$Trans-Sasakian manifolds has been proved under certain conditions.

Keywords: Weakly symmetric, weakly concircular symmetric, weakly Ricci symmetric, weakly concircular Ricci symmetric manifold, $\epsilon$-trans Sasakian manifold.

Shyam Kishor
Department of Mathematics and Astronomy, University of Lucknow, Lucknow, UP, India.
E-mail: skishormath@gmail.com

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 Article Type : Research Article Title : Coincidence Point Theorem Under Mizoguchi-Takahashi Contraction on Ordered Metric Spaces With Application Country : India Authors : Bhavana Deshpande || Amrish Handa || Chetna kothari

Abstract: We construct coincidence point result for $g$ -non-decreasing mappings satisfying Mizoguchi-Takahashi contraction on ordered metric spaces. By using our result, we formulate a coupled coincidence point result for generalized compatible pair of mappings $F,$ $G:X^{2}\rightarrow X.$ We give an example and an application to integral equation to show the usefulness of the obtained results. Our results generalize, modify, improve and sharpen several well-known results.

Keywords: Coincidence point, coupled coincidence point, generalized Mizoguchi-Takahashi contraction, ordered metric space, O-compatible, generalized compatibility, $g$-non-decreasing mapping, mixed monotone mapping.

Bhavana Deshpande
Department of Mathematics, Government P. G. Arts and Science College, Ratlam (M.P.), India.

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 Article Type : Research Article Title : A Multiple Linear Regression Approach for the Analysis of Stress Factors of Faculty in Higher Educational Institutions Country : India Authors : P.Ramesh Reddy || Dr.K.L.A.P.Sarma

Abstract: One of the fast growing sectors in India and abroad is an education sector. This sector masses highly qualified and committed faculty to enhance the quality of education and also to equip the student to meet demand of the industry. In this process faculty has to face many challenges and difficulties to meet the requirements of the education sector. The objective of the present study is under taken to address the effects of different inducing stress factors on job stress of the faculty in higher educational institutions of chittoor district, Andhra Pradesh. Instrument was used in order to get the responses from higher education institutions faculty to achieve the above stated objective. Multiple linear regression and ANOVA were used to analyze the data collected from 500 respondents. Different models were suggested to different categories of faculty members in higher educational institutions to measure their occupational stress and also identified highly contributed factors related to job stress to prevent professional burnout of faculty in higher education.

Keywords: Faculty, Job stress, Multiple linear regression, ANOVA, Higher education.

P.Ramesh Reddy
Research Scholar, Department of Statistics, S.K.university, Anantapuramu, A.P, India.
E-mail: prreddy.sku@gmail.com

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Abstract: A path in an edge−colored graph is said to be a rainbow path if every edge in the path has a different color. An edge colored graph is rainbow connected if there exists a rainbow path between every pair of its vertices. The rainbow connection number of a graph G, denoted by $rc(G)$, is the smallest number of colors required to color the edges of G such that G is rainbow connected. Given two arbitrary vertices u and v in G, a rainbow $u-v$ geodesic in G is a rainbow $u-v$ path of length $d(u, v)$, where $d(u, v)$ is the distance between u and v. G is strongly rainbow connected if there exist a rainbow $u-v$ geodesic for any two vertices u and v in G. The strong rainbow connection number of G, denoted by $src(G)$, is the minimum number of colors required to make G strongly rainbow connected. SyafrizalSyet. al. in \cite{2} proved that, for the sunlet graph $S_n$, $rc(S_n)=src(S_n)=\lfloor\frac{n}{2}\rfloor+n$ for $n\geq2$. In this paper, we improve this result and showthat $rc(S_n)=src(S_n)=\left\{ \begin{array}{ll} n, & \hbox{if n is odd;} \\ \frac{3n-2}{2}, & \hbox{if n is even.} \end{array} \right.$ We also obtain the rainbow connection number and strong rainbow connection number for the line, middle and total graphs of $S_n$