Variational Inequalities Approaches to Minimization Problems with Constraints of Generalized Mixed Equilibria and Variational Inclusions

Abstract

Multistep composite implicit and explicit extragradient-like schemes are presented for solving the minimization problem with the constraints of variational inclusions and generalized mixed equilibrium problems. Strong convergence results of introduced schemes are given under suitable control conditions.

Composite extragradient implicit rule for solving a hierarch variational inequality with constraints of variational inclusion and fixed point problems

“…Our rule is based on the Korpelevich extragradient method, the perturbation mapping, and the W -mappings constructed by {S n } ∞ n=0 . The main results extend and improve some recent results in [14][15][16][17].…”

Generalized Mann Viscosity Implicit Rules for Solving Systems of Variational Inequalities with Constraints of Variational Inclusions and Fixed Point Problems

“…For recent results, we refer the reader to [27][28][29][30][31][32][33][34]. The purpose of this work is to approximate a common solution of GSVI (1), a variational inclusion and a common fixed point problem of a countable family of nonexpansive mappings in spaces with uniformly convex and q-uniformly smooth structures.…”

Iterative Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Pseudocontractive Operators

“…where T : C → C is a pseudocontractive operator. Now, it is well-known that fixed point algorithm of successive approximation is one of the most important techniques in numerical mathematics ( [28][29][30][31][32][33][34][35][36][37][38][39][40]). Focusing on the research with pseudocontractive operators originated in their relations with the important class of monotone operators.…”