Strong Convergence of an Algorithm about Strongly Quasi-Nonexpansive Mappings for the Split Common Fixed-Point Problem in Hilbert Space

Abstract

Based on the recent work by Censor and Segal (2009 J. Convex Anal.16), and inspired by Moudafi (2010 Inverse Problem 26), in this paper, we study the modified algorithm of Yu and Sheng [29] for the strongly quasi - nonexpansive operators to solve the split common fixed-point problem (SCFP) in the framework of Hilbert space. Furthermore we proved the strong convergence for the (SCFPP) by imposing some conditions. Our results extend and improved/developed some recent result announced.

Keywords:  Convex Feasibility, Split Feasibility, Split Common Fixed Point, Strongly Quasi-Nonexpansive Operator, Iterative Algorithm and Strong Convergence.