Random fixed points of \(K\)-set- and pseudo-contractive random maps
type: Item
instance of: scholarly article
title: Random fixed points of \(K\)-set- and pseudo-contractive random maps
zbMATH Open document ID: 1083.47046
author: Nazeer Shahzad
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2004-09-23T00:00:00Z
review text: Let \(M\) be a measurable space, \(X\) a separable Banach space and \(C\) a weakly compact subset of \(X\). Assume that \(T: M\times C\to X\) is a continuous 1-set-contractive random operator. The problem of the existence of random fixed points of \(T\), i.e., the problem of the existence of solutions of the random equation \[ x- T(w,x)= 0,\quad w\in M,\quad x\in X, \] has been considered by many mathematicians. In the paper under review, the author discusses the stochastic solvability of the equation \[ f(w,x)- T(w,x)= 0,\quad w\in M,\quad x\in X, \] where \(f\), \(F\) are continuous random operators. Next, the main result is applied to establish some random fixed point theorems for various classes of \(k\)-set-contractive or so-called pseudo-contractive random operators. In the proofs, some results of Opial, Kuratowski, Ryll-Nardzewski, Petryshyn and Browder are used.
reviewed by: Stefan Czerwik
Mathematics Subject Classification ID: 47H40
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47H09
zbMATH DE Number: 2102564
zbMATH Keywords: random operator
zbMATH Keywords: random fixed point
zbMATH Keywords: weak upper limit
zbMATH Keywords: measurable selector
MaRDI profile type: Publication
full work available at URL: j.na.2004.02.006
OpenAlex ID: W2084726522
cites work: Applications of the proximity map to random fixed point theorems in Hilbert spaces
cites work: Random fixed points of set-valued operators
cites work: Semicontractive and semiaccretive nonlinear mappings in Banach spaces
cites work: Fixed Point Theorems for Lipschitzian Pseudo-Contractive Mappings
cites work: Measurability and integrability of the weak upper limit of a sequence of multifunctions
cites work: A random fixed point theorem for a multivalued contraction mapping
cites work: Random fixed point theorems with an application to random differential equations in Banach spaces
cites work: Q5531649
cites work: Random Approximations and Random Fixed Point Theorems for Continuous 1-Set- Contractive Random Maps
cites work: Some random approximations and random fixed point theorems for 1-set-contractive random operators
cites work: Weak convergence of the sequence of successive approximations for nonexpansive mappings
cites work: Q3184915
cites work: Fixed points and random fixed points for weakly inward approximable maps
cites work: Random Fixed Point Theorems for Measurable Multifunctions in Banach Spaces
cites work: Random fixed points and random differential inclusions
cites work: Fixed Point Theorems for Various Classes of 1-Set-Contractive and 1-Ball- Contractive Mappings in Banach Space
cites work: Random fixed points and viable random solutions of functional- differential inclusions
cites work: Some Random Fixed Point Theorems for Condensing Operators
cites work: Random fixed point theorems for various classes of 1-set-contractive maps in Banach spaces
cites work: Random fixed points of set-valued maps
cites work: Random fixed points for several classes of 1-ball-contractive and 1-set-contractive random maps
DOI: 10.1016/J.NA.2004.02.006
description: scientific article; zbMATH DE number 2102564