General iterative algorithms approachto variational inequalities and minimum-norm fixed point for minimization and split feasibility problems

Abstract

In this paper, we introduce general iterative algorithms for finding a fixed point of a nonexpansive mapping T, which is a unique solution of some variational inequalities. Also, we prove some strong convergence theorems to a fixed point of T under different control conditions in Hilbert spaces by using the proposed algorithms, which is a minimum-norm fixed point of T. Furthermore, we apply our results to show the existence of solutions for the minimization problems and split feasibility problems. The main results in this paper extend and improve the recent ones announced by many others.