Convergence results for stochastic split feasibility problem using Perturbed Mann iterative scheme in Hilbert space

Abstract

The focus of this study is on the stochastic split feasibility problem as an extension to deterministic (classical) split feasibility problem. Stochastic convergence in the quadratic mean of an iteration based on Perturbed Mann-type iterative scheme for solving the stochastic split feasibility problem is proven. The Lipschitzian and Pseudo-contractive mapping of the operators in Hilbert space was adopted. A convergence in quadratic mean to a random fixed-point of a split feasibility problem was achieved.