An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings

2021 ◽  
Author(s):  
Timilehin Opeyemi Alakoya ◽  
Adeolu Taiwo ◽  
Oluwatosin Temitope Mewomo ◽  
Yeol Je Cho
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Convex Minimization ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

scholarly journals An iterative algorithm for the system of split mixed equilibrium problem

2020 ◽  
Vol 53 (1) ◽  
pp. 309-324
Author(s):  
Ibrahim Karahan ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Equilibrium System ◽  
Convergence Conditions ◽  
Mixed Equilibrium Problems ◽  
Split Variational Inequality ◽  
Mixed Equilibrium ◽  
Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

scholarly journals A Hybrid Iterative Scheme for a Maximal Monotone Operator and Two Countable Families of Relatively Quasi-Nonexpansive Mappings for Generalized Mixed Equilibrium and Variational Inequality Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-31 ◽  
Author(s):  
Siwaporn Saewan ◽  
Poom Kumam
Keyword(s):  
Banach Space ◽  
Variational Inequality ◽  
Monotone Operator ◽  
Maximal Monotone Operator ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Maximal Monotone ◽  
Generalized Mixed Equilibrium Problem ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality for anα-inverse-strongly monotone operator, the set of solutions of the generalized mixed equilibrium problem and zeros of a maximal monotone operator in the framework of a real Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2 uniformly convex and uniformly smooth Banach space. The results presented in this paper improve and extend some recent results.

scholarly journals Extragradient algorithms for variational inequality, fixed point and generalized mixed equilibrium problems

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1021-1030
Author(s):  
Baohua Guo ◽  
Lijuan Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Weak Convergence ◽  
Variational Inequalities ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Generalized Mixed Equilibrium Problems ◽  
Mixed Equilibrium Problems ◽  
Generalized Mixed Equilibrium ◽  
Mixed Equilibrium

The purpose of this paper is to investigate variational inequalities, fixed point problems and generalized mixed equilibrium problems. Anextragradient iterative algorithm is investigated in the framework of Hilbert spaces. Weak convergence theorems for common solutions are established.

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