Hybrid Extragradient-Like Viscosity Methods for Generalized Mixed Equilibrium Problems, Variational Inclusions, and Optimization Problems

Hybrid-extragradient Type Methods for a Generalized Equilibrium Problem and Variational Inequality Problems of Nonexpansive Semigroups

We study and introduce modified mann iterative algorithms for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of variational inequalities and the set of fixed points for nonexpansive semigroups. Then, we prove strong convergence theorems in a real Hilbert space by using the hybrid-extragradient type methods in the mathematical programm...

Vector Optimization Problems and Generalized Vector Variational-Like Inequalities

In this paper, some properties of  pseudoinvex functions, defined by means of  limiting subdifferential, are discussed. Furthermore, the Minty vector variational-like inequality,  the Stampacchia vector variational-like inequality, and the  weak formulations of these two inequalities  defined by means of limiting subdifferential are studied. Moreover, some relationships  between the vector vari...

A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems

In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces. It is shown that the sequence generat...

Iterative Methods for Equilibrium Problems, Variational Inequalities and Fixed Points

A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the a...