## Issue 4 − FVolume 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 : Locally Linear Convex Maps and H-derivation Country : Italy Authors : Franco Fineschi

Abstract: Linear convex maps are considered. The linearity of a map is related to a point. The space of functions with this property and the analytic form is obtained. A new polynomial for a function improves the convergence.

Keywords: Linearity, convex, h-derivation.

Franco Fineschi
Department DISAG, University of Siena, Piazza S.Francesco, 53100 Siena, Italy.
E-mail: franco.fineschi@unisi.it

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 Article Type : Research Article Title : Employing weak $\psi-\varphi$ Contraction in Common Coupled Fixed Point Results for Hybrid Pairs of Mappings Satisfying (EA) Property Country : India Authors : Bhavana Deshpande || Amrish Handa || Chetna Kothari

Abstract: We establish some common coupled fixed point theorems for two hybrid pairs of mappings under weak $\psi -\varphi$ contraction on a non complete metric space, which is not partially ordered. It is to be noted that to find coupled coincidence point, we do not employ the condition of continuity of any mapping involved therein. An example is also given to validate our results.

Keywords: Coupled fixed point, coupled coincidence point, weak $\psi -\varphi$ contraction, $w-$compatibility, $F-$weakly commutativity.

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

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 Article Type : Research Article Title : Harmonised Fractal dimensional Measure: A Special Case of a Haar Measure and Convenience With Martingales Country : Nigeria Authors : Bright O.Osu || Obiageri E.Ogwo

Abstract: The Martingale's property is one of the fundamental mathematical properties which underline many important results in finance, obeying the principle of risk neutral pricing and a necessary condition for an efficient market. The aim of this paper is to show that the Harmonized fractal dimensional measure (HFDM) is a special case of a Haar measure and also convenience with martingale measure. To establish this, we first transform the measure into a solution then checkmate it under the Martingale properties. In this sense, the efficiency of harmonized fractal dimensional measure in capital market connotes that the measure is a martingale as it deals with wealth distribution that are highly skewed, curbs investment by neutralizing risky assets and diverting the wealth to consumption.

Keywords: Borel Sets, Haar Measure, Harmonized integral transform, Market efficiency and Martingales.

Bright O.Osu
Department of Mathematics, Abia State University, Uturu, Abia State, Nigeria.
E-mail: megaobrait@hotmail.com

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 Article Type : Research Article Title : Generalization of Pairwise Weakly Continuous Functions Country : India Authors : R.Suganya || N.Rajesh

Abstract: As a generalization of $\delta$-$b$-continuous functions, we introduce the notion of weakly $\delta$-$b$-continuous functions in bitopological spaces and obtain several characterizations and some properties of weakly $\delta$-$b$-continuous functions.

Keywords: Bitopological spaces, $(i, j)$-$\delta$-$b$-open sets, weakly $(i, j)$-$\delta$-$b$-continuous function.

N.Rajesh
Department of Mathematics, Rajah Serfoji Government College, Thanjavur, Tamilnadu, India.
E-mail: nrajesh\_topology@yahoo.co.in

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 Article Type : Research Article Title : The Maximum Independent Vertex Energy of a Graph Country : India Authors : K.B.Murthy || Puttaswamy || A.M.Naji

Abstract: In a graph $G=(V, E)$, A set $I\subseteq V$ is an independent vertex set if no two vertices in $I$ are adjacent. The number of vertices in a maximum independent set in a graph $G$ is the independence number (or vertex independence number) of $G$ and is denoted by $\beta(G)$. In this paper, we study the maximum independent vertex energy, denoted by $E_I(G)$, of a graph $G$. We are compute the maximum independent energies of complete graph, complete bipartite graph, star graph, cocktail party graph and Friendship graph. Upper and lower bounds for $E_I(G)$ are established.

Keywords: Independent set, independence number, maximum Independent matrix, maximum Independent eigenvalues, maximum Independent energy.

A.M.Naji
Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysuru, India.
E-mail: ama.mohsen78@gmail.com

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 Article Type : Research Article Title : On Non-Vacuum Static Spherically Symmetric Solution in $f(R)$ Theory of Gravity in $V_5$ Country : India Authors : P.O.Bagde || K.T.Thomas

Abstract: In this paper, we studied non-vacuum static spherically symmetric solution of the field equation in metric gravity using dust matter and constant Ricci scalar curvature in five-dimensions. The density of dust matter and the function of the Ricci scalar curvature will also be evaluated at constant scalar curvature.

Keywords: $f(R)$ theory of gravity, Spherically symmetric solutions, non-vacuum solution, higher dimension.

P.O.Bagde
Assistant Professor, Department of Mathematics, RCOEM, Nagpur, India.
E-mail: prafulla.bagde@gmail.com

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 Article Type : Research Article Title : Radius of $p$-valent Strong Starlikeness for Certain Class of Analytic Functions Country : India Authors : A.Gangadharan || S.Chinthamani || B.Srutha Keerthi

Abstract: This paper deals with $p$-valent strongly starlikeness of the class $SP(\alpha, A, B)$ satisfying the subordination $e^{i \alpha} \frac{zf^\prime(z)} {f(z)} \prec cos \ z \frac{1+Az} {1+Bz} + i \ sin \ \alpha,$ $f \in A$, $z \in \Delta$, $0 \leq \alpha < 1$, $-1 \leq B < A \leq 1$. We are concerned with computing the radius results for the above mentioned class and the results that we obtained are generalizations of earlier results obtained previously by different authors.

Keywords: Radius problem, subordination, analytic function, radius of starlikeness, strong starlikeness and radius of $p$-valent strongly starlikeness.

S.Chinthamani
Research Scholar, Anna University, Chennai, Tamilnadu, India.
E-mail: chinvicky@rediffmail.com

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 Article Type : Research Article Title : Efficient Estimator of Population Variance Using Coefficient of Kurtosis and Population Mean of Auxiliary Variable Country : India Authors : S.K.Yadav || Ravendra Kumar || S.Kumar || S.Verma || S.Kumar

Abstract: In the present paper an efficient estimator of population variance of study variable has been proposed using knowledge of coefficient of kurtosis and the population mean of the auxiliary variable. The bias and the mean squared error of the proposed variance have been obtained up to the first order of approximation. The optimum value of the characterizing scalar, which minimizes the mean squared error, has been obtained. The minimum value of the mean squared error has been obtained for this optimum value of the characterizing scalar. A comparison has been done with the mentioned existing estimators of population variance. An empirical study is also carried out to judge the performance of the proposed estimator along with the other estimators of population variance.

Keywords: Main variable, auxiliary variable, bias, mean squared error, efficiency.

Ravendra Kumar
Department of Mathematics, Dr Ram Manohar Lohiya Government Degree College, Aonla, Bareilly, U.P., India.
E-mail: rkpmbly@gmail.com

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 Article Type : Research Article Title : Study of Common Fixed Point Theorems in Fuzzy Normed Spaces Country : India Authors : Trapti Awasthi || S.S.Rajput

Abstract: In this paper, we prove some common fixed point theorems in fuzzy normed spaces also we give an example of fuzzy normed space which is not a fuzzy metric space. By using common property (E.A.) we prove some common fixed point theorem in fuzzy normed spaces which are generalizations of many known results of (\cite{a3, REF:Imdad_Ali2006, a1,a2,a4, REF:Singh_Jain_Ganita05,REF:Vetro_Vetro2008}) and cited their in.

Keywords: Fuzzy normed space, property (E.A.), common property (E.A.), common fixed point, generalized fuzzy contraction.

Trapti Awasthi
Department of Mathematics, Shri Satya Sai University of Technology, Sehore, M.P., India.
E-mail: traptiawasthimath@gmail.com

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