Abstract
The main purpose of this paper is to prove a random fixed point theorem in a separable Banach space equipped with a complete probability measure for a certain class of contractive mappings. The main finding of this paper is the identification of some random fixed point theorems and the relevant application with appropriate supporting examples. A random fixed point theorem is useful to determine the existence of a solution in a Banach space of a random nonlinear integral equation. MSC:47H10, 60H25.
Highlights
1 Introduction The application of fixed point theory in different branches of mathematics, statistics, engineering and economics relating to problems associated with approximation theory, theory of differential equations, theory of integral equations, etc. has been recognized in the existing literature [, ] and [ ]
After the initial impetus given by the Prague school of Probability in s, considerable attention has been given to the study of random fixed point theorems
Padgett [ ] applied a random fixed point theorem to prove the existence of a solution in a Banach space of a random nonlinear integral equation
Summary
The application of fixed point theory in different branches of mathematics, statistics, engineering and economics relating to problems associated with approximation theory, theory of differential equations, theory of integral equations, etc. has been recognized in the existing literature [ , ] and [ ]. Špaček [ ] and Hanš [ , ] first proved random fixed point theorems for random contraction mappings on separable complete metric spaces.
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