Hybrid Steepest Descent Method of One-parameter Nonexpansive Cosine Families for Variational Inequality Problems in Hilbert Spaces

Nimit Nimana, Somboon Niyom, Narin Petrot

Abstract

The purpose of this paper is to present the  hybrid steepest descent method for solving the variational inequality problems over the common fixed point set of  a one-parameter strongly continuous nonexpansive cosine family in the context of Hilbert spaces. Under some suitable assumptions, imposed upon the control parameters, we have established the strong convergence theorems for the presented methods.