scholarly journals The common solution for a generalized equilibrium problem, a variational inequality problem and a hierarchical fixed point problem

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Ibrahim Karahan ◽  
Aydin Secer ◽  
Murat Ozdemir ◽  
Mustafa Bayram
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Hierarchical Fixed Point ◽  
Generalized Equilibrium ◽  
The Common

scholarly journals Inertial KM-type extragradient scheme for solving a variational inequality and a hierarchical fixed point problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ghada AlNemer ◽  
Rehan Ali ◽  
K. R. Kazmi
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequality Problem ◽  
Nonexpansive Mappings ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Iterative Schemes ◽  
Common Solution ◽  
Hierarchical Fixed Point ◽  
Hierarchical Fixed Point Problems

AbstractWe propose an inertial KM-type extragradient scheme to approximate a common solution of a variational inequality problem and a hierarchical fixed point problem for nonexpansive mappings. This scheme generalizes and unifies a number of known iterative schemes. Furthermore, we discuss the weak convergence for the proposed scheme. We also discuss an example to illustrate the main theorem.

scholarly journals Approximation of common solutions for a fixed point problem of asymptotically nonexpansive mapping and a generalized equilibrium problem in Hilbert space

2019 ◽  
Vol 27 (1) ◽  
Author(s):  
Richard Osward ◽  
Santosh Kumar ◽  
Mengistu Goa Sangago
Keyword(s):  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Equilibrium Problem ◽  
Fixed Point Problem ◽  
Asymptotically Nonexpansive Mapping ◽  
Point Problem ◽  
Generalized Equilibrium Problem ◽  
Common Solution ◽  
Asymptotically Nonexpansive ◽  
Generalized Equilibrium

Abstract In this paper, we introduce an iterative algorithm to approximate a common solution of a generalized equilibrium problem and a fixed point problem for an asymptotically nonexpansive mapping in a real Hilbert space. We prove that the sequences generated by the iterative algorithm converge strongly to a common solution of the generalized equilibrium problem and the fixed point problem for an asymptotically nonexpansive mapping. The results presented in this paper extend and generalize many previously known results in this research area. Some applications of main results are also provided.

scholarly journals Triple Hierarchical Variational Inequalities, Systems of Variational Inequalities, and Fixed Point Problems

Mathematics ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 187
Author(s):  
Lu-Chuan Ceng ◽  
Qing Yuan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Variational Inequalities ◽  
General System ◽  
Inequality Constraint ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Common Solution ◽  
Common Fixed Point Problem ◽  
Monotone Variational Inequality

In this paper, we introduce a multiple hybrid implicit iteration method for finding a solution for a monotone variational inequality with a variational inequality constraint over the common solution set of a general system of variational inequalities, and a common fixed point problem of a countable family of uniformly Lipschitzian pseudocontractive mappings and an asymptotically nonexpansive mapping in Hilbert spaces. Strong convergence of the proposed method to the unique solution of the problem is established under some suitable assumptions.

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