On convergence of random fixed point SP iterative scheme with errors using three random operators

Renu Chugh,Satish Narwal,Vivek Kumar

doi:10.12988/imf.2014.312245

Abstract

The aim of this article is to establish the convergence and almost stability results of random SP fixed point iterative scheme with errors using three asymptotically quasi-nonexpansive type random operators in a real separable Banach space. The results presented in this paper generalize several well known results in Banach spaces. Mathematics Subject Classification: 47H10, 54 H25

Highlights

Introduction and PreliminariesApproximation of fixed points was studied by several authors in deterministic fixed point theory[6,7,8,9,13,16,17,20,22,23,24,25,27,30,31]
Several general iterative schemes have been successfully applied for solutions of operator equations
The development of random fixed point iterations was initiated by Choudhury in [10,11,12], where random Ishikawa iteration scheme was defined and its strong convergence to a random fixed point in Hilbert spaces was discussed

Summary

Introduction

Introduction and PreliminariesApproximation of fixed points was studied by several authors in deterministic fixed point theory[6,7,8,9,13,16,17,20,22,23,24,25,27,30,31]. A measurable function p : Ω → X is said to be a random fixed point of the random operator T : Ω× X → X if T (t, p (t )) = p (t ) for all t ∈ Ω . Random Ishikawa iterative scheme [12]: xn+1 ( w) = (1− αn )xn (w) + αnT ( w, yn (w)) , yn (w) = (1− βn ) xn (w) + βnT (w, xn (w)), for n > 0, w∈ Ω, where 0 ≤ αn ,βn ≤ 1 and x0 : Ω → F is an arbitrary measurable mapping.

Objectives

Results

Conclusion