An algorithm for nonlinear problems with variational inequality methods

The purpose of this paper is to introduce a mapping in the framework of a 2-uniformly smooth and uniformly convex Banach space and obtain a common solution for the fixed point set of finite families of βi -enriched non-expansive mappings and ( Ψ , βi )-enriched strictly pseudocontractive mappings. Two solution sets of variational inequality problems are also given. Moreover, we prove several strong convergence theorems for the fixed point set of the finite family of ( Ψ , βi )-enriched strictly pseudocontractive mappings and the solution set of variational inequality problems. By using the famous Mann-Halpern type iterative method we obtain some strong convergence theorems. Our results from this paper improve and generalize many well-known results in the existing literature.