Strong convergence theorems for finding a common solution of a variational inequality problem and a fixed point problem in a uniformly convex and 2-smooth Banach spaces

Abstract

In this paper, we generalize α-inverse strongly accretive mapping to accretive and Lipschitz continuous mapping in uniformly convex and 2-smooth Banach space and prove a strong convergence result for finding common element of the set of fixed points of strictly pseudocontractive mappings and the set of solutions of variational inequality problem. With the help of an example, we find a common solution of a variational inequality problem and a fixed point problem.