Random fixed point of Meir-Keeler contraction mappings and its application

Subject Areas : Applied Mathematics

H. Dibachi ¹

1 - Department of Mathematics, Islamic Azad University, Arak-Branch, Arak, Iran.

Received: 2015-09-30 Accepted : 2015-09-30 Published : 2013-05-01

Keywords: Random fixed point, Meir-Keeler contraction, measurable space, L-􀀀function,

Abstract :

In this paper we introduce a generalization of Meir-Keeler contraction forrandom mapping T : Ω×C →C, where C be a nonempty subset of a Banachspace X and (Ω,Σ) be a measurable space with  being a sigma-algebra of sub-sets of. Also, we apply such type of random fixed point results to prove theexistence and unicity of a solution for an special random integral equation.

References:

[1] A. Meir, E. Keeler. A theorem on contraction mapping, J. Math. Anal. Appl.
28 (1969), 326-329.
[2] A. Branciari. A xed point theorem for mapping satisfying a general contractive
condition of integral type, Int. J. Math. Math. Sci. 29 (2002), 531-536.
[3] I. Beg, Minimal displacement of random variables under lipschitz random maps,
Topological Methods in Nonlinear Analysis Journal of the Juliusz Schauder Cen-
ter 19(2002), 391397
[4] S. Plubtieng, P. Kumam, R. Wangkeeree, Approximation of a common random
xed point for a nite family of random operators, Inter. J. Math. Math. Sci.
Volume 2007, Article ID 69626, 12 pages