# Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations

## TL;DR

This paper establishes new random fixed point theorems for Hardy-Rogers operators in Banach spaces and applies these results to demonstrate solutions for random integral equations, extending deterministic fixed point results to stochastic settings.

## Contribution

It introduces novel random fixed point theorems for Hardy-Rogers operators and applies them to solve random nonlinear integral equations in Banach spaces.

## Key findings

- Existence of solutions for certain random nonlinear integral equations.
- Extension of deterministic fixed point theorems to stochastic frameworks.
- Development of stochastic versions of Hardy-Rogers fixed point theorems.

## Abstract

In this paper, we prove some random fixed point theorems for Hardy-Rogers self-random operators in separable Banach spaces and, as some applications, we show the existence of a solution for random nonlinear integral equations in Banach spaces. Some stochastic versions of deterministic fixed point theorems for Hardy-Rogers self mappings and stochastic integral equations are obtained.