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

Abstract

In this work, strong convergence and stability results of a three step random iterative scheme with errors for strongly pseudo-contractive Lipschitzian maps are established in real Banach spaces. Analytic proofs are supported by providing numerical examples. Applications of random iterative schemes with errors to find solution of nonlinear random equation are also given. Our results improve and establish random generalization of results obtained by Xu

Random iterative algorithms and almost sure stability in Banach spaces

“…The study of nonlinear operators has attracted the attention of many mathematicians in various spaces (see [2, 13-15, 18, 30, 32, 33] and references therein). Several interesting random fixed point results have been established in [4,6,8,13,15,18,19,27,34]. If the exact value of a fixed point of a mapping cannot be found, we approximate it through a convenient iterative algorithm.…”

“…If the exact value of a fixed point of a mapping cannot be found, we approximate it through a convenient iterative algorithm. With the developments in random fixed point theory, there has been a renewed interest in random iterative algorithms [4,6,8,13,27,34]. In linear spaces, Mann and Ishikawa iterative algorithms have been extensively applied to fixed point problems [5,16,25,29].…”

Convergence and stability of an iterative algorithm for strongly accretive Lipschitzian operator with applications

“…Chugh and Kumar [7] studied strong convergence and almost stability of SP iterative algorithm with mixed errors for the accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach spaces. Recently, Chugh et al [8] and Hussain et al [12] proved some strong convergence results of iterative algorithms. In computational mathematics, a fixed point iterative algorithm is valuable and useful for applications if it satisfies the following conditions:…”

“…Variational inclusions, generalization of variational inequalities, have been widely studied [4,11]. One of the most interesting and important problems in the theory of variational inclusions is the development of an efficient and implementable iterative algorithm [4,11,12]. Let T, A : X → X, : X → X * be mappings on a real reflexive Banach space X, X * is dual of X and •, • denotes pairing of X and X * .…”

Exponential inequalities for Mann’s iterative scheme with functional random errors

“…In [4], a random fixed point theorem was obtained for the sum of a weaklystrongly continuous random operator and a nonexpansive random operator which contains as a special Krasnoselskii type of Edmund and O'Regan via the method of measurable selectors. We note some recent works on random fixed points in [1,3,5,13,14,16,27].…”