Halpern's Iteration Process for Multiple Sets Split Common Fixed Point of Quasi-Nonexpansive Mappings (Study on Nonlinear Analysis and Convex Analysis)

Abstract

In this paper, we consider iteration processes of Halpern's type to find fixed point of quasi-nonexpansive mapping and common element of solution for the split common fixed point of quasi-nonexpansive mappings. We establish strong convergence theorems of this problems. We apply our results to study the common element of solution of multiple split fixed point problems for quasi-nonexpansive mappings. We also apply our result to study common element of solution for the equilibrium problem and the fixed point of generalized hybrid mapping. Our result gives an partial answer to two open questions which were given by Chidume and Chidume [11], and Kurokawa and Takahashi[12].