Iterative Methods for Split Common Fixed Point Problems in Banach Spaces and Applications (Nonlinear Analysis and Convex Analysis)

Abstract

In this article, motivated by split feasibility problems and split common null point problems in Hilbert spaces, we first introduce the concept of nonlinear operators in Banach spaces which covers strict pseud-contractions and generalized hybrid mappings in Hilbert spaces, and the metric projections and the metric resolvents in Banach spaces. Then we consider split common fixed point problems with the operators in Banach spaces. Using hybrid methods, Mann s type iterations and Halpern s type iterations, we prove weak and strong convergence theorems for finding solutions of split common fixed point problems in Banach spaces. Furthermore, using these results, we get well-known and new results which are connected with split feasibility problems and split common null point problems in Banach spaces.