HYBRID STEEPEST DESCENT METHOD FOR SPLIT VARIATIONAL INCLUSION AND FINITE FAMILY OF NONEXPANSIVE MAPPINGS

Abstract

In the present paper, we use hybrid steepest descent method for finding a common point of the solution set of split variational inclusion and the fixed points set of a finite family of nonexpansive mappings in Hilbert spaces. Further, we prove that the sequences generated by our iterative algorithm converge strongly to the common point, which is the unique solution of a variational inequality. Our result improves and extends the corresponding results announced by many others. At the end of the paper, we extend our result to the more broad family of λ-strictly pseudo-contractive mappings.