Hybrid Projection Algorithm for a New General System of Variational Inequalities in Hilbert Spaces

Abstract EN

A new general system of variational inequalities in a real Hilbert space is introduced and studied.

The solution of this system is shown to be a fixed point of a nonexpansive mapping.

We also introduce a hybrid projection algorithm for finding a common element of the set of solutions of a new general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space.

Several strong convergence theorems of the proposed hybrid projection algorithm are established by using the demiclosedness principle.

Our results extend and improve recent results announced by many others.