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Issue 4 − A
Volume 3 (2015)

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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.

E-mail: bhavnadeshpande@yahoo.com

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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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Article Type |
: | Research Article |

Title |
: | Rainbow Connection Number of Sunlet Graph and its Line, Middle and Total Graph |

Country |
: | India |

Authors |
: | K.Srinivasa Rao || R.Murali |

**Abstract: ** A path in an edgeâˆ’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 $S_n$

**Keywords: ** Rainbow connection number, sunlet graph, line graph, middle graph and total graph.

K.Srinivasa Rao

Department of Mathematics, Shri Pillappa College of Engineering, Bangalore, India.

E-mail: srinivas.dbpur@gmaill.com