Strong convergence theorems for fixed point problems for strict pseudo-contractions and variational inequalities for inverse-strongly accretive mappings in uniformly smooth Banach spaces

Abstract

In this paper, we first study a simple viscosity iterative algorithm for finding a fixed point of a nonexpansive mapping in uniformly smooth Banach space and obtain a strong convergence theorem under suitable conditions. Then, we apply our iterative algorithm to find a common element of the set of fixed points for a strict pseudo-contraction and the set of fixed points for a nonexansive mapping in uniformly smooth Banach space. We also apply our main results to find a common element of the set of fixed points for strict pseudo-contraction and nonexpansive mapping, the set of solutions of general variational inequalities for two inverse-strongly accretive mappings and equilibrium problems in uniformly smooth Banach spaces or Hilbert spaces. Finally, two numerical examples are given in support of our main results.