Nonlinear iterative algorithms for solving variational inequality problems over the set of common fixed point of one-parameter nonexpansive semigroup and demicontractive mappings

Abstract

In this paper, we propose a practical iterative method for solving variational inequality problem over the set of common fixed point of one-parameter nonexpansive semigroup and demicontractive mappings in a real Hilbert space. In a first step, we prove that this variational inequality problem admit one and a unique solution. Secondly, we deduced an iterative algorithm that converges strongly to the solution. Finally, we will apply these results to study some nonlinear problems.