The hybrid algorithm for the system of mixed equilibrium problems, the general system of finite variational inequalities and common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings

Abstract

In this article, we introduce a new iterative algorithm by the shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of general system of finite variational inequalities, the set of solutions of fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Our results improve and extend the corresponding recent results in literature work.

A Viscosity Hybrid Steepest Descent Method for Equilibrium Problems, Variational Inequality Problems, and Fixed Point Problems of Infinite Family of Strictly Pseudocontractive Mappings and Nonexpansive Semigroup

“…where is a -inverse-strongly monotone mapping, { } is a sequence in (0, 1), and { } is a sequence in (0, 2 ). They showed that if ( ) ∩ VI( , ) ̸ = 0, then the sequence { } generated by (17) converges weakly to some ∈ ( ) ∩ VI( , ).…”