Random Fixed Points and Random Approximations in Nonconvex Domains

Abstract

Stochastic generalizations of some fixed point theorems on a class of nonconvex sets in a locally bounded topological vector space are established. As applications, Brosowski-Meinardus type theorems about random invariant approximation are obtained. This work extends or provides stochastic versions of several well known results.

Comments on the Papers Arch. Math. Brno, 422006, 51-58 - Thai J. Math., 32005, 63-70 and Math. Communications 132008, 85-96

“…The measurability of T n is still an open problem(see [2,13] and references therein). Thus all the results, Theorems 3.1-3.3 in [17], are deterministic in nature and hence are simple corollaries to more general results in [5,6,10,11].…”

Some Strong Convergence Results of Random Iterative Algorithms With Errors in Banach Spaces

“…With the recent rapid developments in random fixed point theory, there has been a renewed interest in random iterative schemes [5,6,7,22,23,24,26]. In linear spaces, Mann and Ishikawa iterative schemes are two general iterative schemes which have been successfully applied to fixed point problems [1,2,13,14].…”

On convergence of random iterative schemes with errors for strongly pseudo-contractive Lipschitzian maps in real Banach spaces

“…The machinery of fixed point theory provides a convenient way of modelling many problems arising in non-linear analysis, probability theory and for a solution of random equations in applied sciences, see [4,9,11,12,15,17,18,20,21,25,27,29,30,31,33,34,35,36,38,39,40] and references there. With the developments in random fixed point theory, there has been a renewed interest in random iterative schemes [2,3,7,8,10].…”