iosr-Jm   Volume-5 ~ Issue-6

Abstract: The aim of this paper is to prove a common fixed point theorem which generalizes the result of Brian Fisher [1] and etal. by weaker conditions. The conditions of continuity, compatibility and completeness of a metric space are replaced by weaker conditions such as reciprocally continuous and compatible, weakly compatible, and the associated sequence.

Keywords: Fixed point, self maps, reciprocally continuous, compatible maps, weakly compatible mappings.

[1] B.Fisher and etal, "Common Fixed Point Theorems for compatible mappings", Internat.J. Math. & Math. Sci, 3(1996), 451-456.

[2] G .Jungck, "Compatible Mappings and Common Fixed Points", Inst. J. Math. Math. Sci .9(1986), 771-779.

[3] G.Jungck, B.E. Rhoades, Fixed Point for set valued Functions without Continuity, Indian.J. Pure.Appl.Math,3(1998), 227-238.

[4] G. Jungck., B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure.Appl.Math, 3 (1998), 227-238.

[5] V.Srinivas, R.Umamaheshwar Rao ,A Fixed point Theorem for Weekly Compatible Mappings , Journal of Mathematical Sciences & Engineering Applications,1(2007),41-48.

[6] V.Srinivas, R.Umamaheshwar Rao, Common Fixed Point Theorem for Four Self Maps, International Journal of Mathematics Research, 2(2011 ),113-118.

Abstract: In this paper we discussed the stability of the null solution of the second order differential equation . Under some unusual assumptions we obtain new stability results for this classical equation.

[1] Bellman.R.,Staility Theory of Differential Equations,McGraw-Hill,New York
[2] Burton T.A, and Furumochi,Tetsuo (2001) Fixed points and prolem in stability Theory for ordinary and functional Differential quations, Dynamical System. April 10, 89-116
[3] Burton T.A, and Furumochi,Tetsuo (2002) Asymptotic behaviour of solution of functional Differential Equations, by fixed point theorem Dynamical system 11,499-519.
[4] Burton T.A, and Furumochi,Testuo (2002) Krasnoselskiis fixed point theorem and stability of nonlinear Analysis 49, 445-454.
[5] Burton T.A, and Furumochi,Testuo (2005) Asymptotic behaviour of non linear functional Differential Equations, by Schauder's theorem Nonlinear Stud. 12,73-84.
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Abstract:The field equations for perfect fluid coupled with mass less scalar field are solved with conditions 𝑝=𝜌 𝑎𝑛𝑑 𝑅=𝑘𝐴𝑛 (where k and n both are constant.) for five dimensional space-time in General Theory of Relativity. Also various physical and geometrical properties of the model have been discussed. Keywords - Five dimensional space-time, mass less scalar field, perfect fluid.

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