Point Theorems For Random Operators Research Articles

Random Fixed Point Theorems and Applications to Random First-Order Vector-Valued Differential Equations

In this paper, we establish several random fixed point theorems for random operators satisfying some iterative condition w.r.t. a measure of noncompactness. We also discuss the case of monotone random operators in ordered Banach spaces. Our results extend several earlier works, including Itoh’s random fixed point theorem. As an application, we discuss the existence of random solutions to a class of random first-order vector-valued ordinary differential equations with lack of compactness.

Random fixed point theorems under weak topology features and application to random integral equations with lack of compactness

We present several random fixed point theorems for random operators with deterministic or stochastic domains. The main assumptions of our results are formulated in terms of the weak topology and an axiomatic definition of the measure of weak noncompactness. The results herein extend in a broad sense some new and classical results in the literature. As an application, we discuss the solvability of a random Hammerstein integral equation with lack of compactness.

Random fixed points of completely random operators

The purpose of this paper is to examine the notion of completely random operators and to prove some random fixed point theorems for such operators. Unlike many random fixed point theorems for random operators, it seems to be impossible to obtain them from deterministic fixed point theorems.

Measures of noncompactness and fixed points of random operators

Abstract : The purpose of this paper is to consider some measures of noncompactness and their application to fixed point theorems for random operators. In a subsequent paper we will consider applications of these results to random operator equations. This paper is not the first to consider measures of noncompactness in probabilistic analysis. We refer to the book of Constantin and Istratescu for results on measures of noncompactness and probabilistic metric spaces. Section 2 gives some basic definitions of measures of noncompactness, and lists their properties. Section 3 is devoted to applications of measures of noncompactness to fixed point theorems for random operators. Keywords include: Operators (Mathematics), Probability, Noncompactness.