Algorithmic and analytical approach to the proximal split feasibility problem and fixed point problem

Abstract

In this paper, we investigate the proximal split feasibility algorithm  and fixed point problem in Hilbert spaces. We propose an iterative algorithm for finding a common element of the solution of the proximal split feasibility algorithm  and fixed point of an $L$- Lipschitz pseudocontractive operator. We demonstrate that the considered algorithm converges strongly to a common point of the investigated problems under some mild conditions.