FIXED POINT SOLUTION METHODS FOR SOLVING EQUILIBRIUM PROBLEMS

In this paper, we introduce an iterative algorithm for finding a common solution of a finite family of the equilibrium problems, quasi-variational inclusion problems and fixed point problem on Hadamard manifolds. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in literature.

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Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

Abstract and Applied Analysis ◽

10.1155/2014/580621 ◽

2014 ◽

Vol 2014 ◽

pp. 1-7

Author(s):

Jinlu Li ◽

Ying Liu ◽

Hongya Gao

Keyword(s):

Fixed Point ◽

Fixed Point Theorem ◽

Topological Structure ◽

Fixed Point Theorems ◽

Equilibrium Problems ◽

Saddle Points ◽

Order Relation ◽

Partial Order Relation ◽

Chain Complete ◽

Set Valued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

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New Contribution to the Advancement of Fixed Point Theory, Equilibrium Problems, and Optimization Problems

Journal of Applied Mathematics ◽

10.1155/2013/895439 ◽

2013 ◽

Vol 2013 ◽

pp. 1-1 ◽

Cited By ~ 3

Author(s):

Wei-Shih Du ◽

Erdal Karapınar ◽

Lai-Jiu Lin ◽

Gue Myung Lee ◽

Tamaki Tanaka

Keyword(s):

Fixed Point ◽

Equilibrium Problems ◽

Optimization Problems ◽

Fixed Point Theory ◽

Point Theory

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Hybrid Bregman projection methods for fixed point and equilibrium problems

Carpathian Journal of Mathematics ◽

10.37193/cjm.2018.03.21 ◽

2018 ◽

Vol 34 (3) ◽

pp. 441-447

Author(s):

ZI-MING WANG ◽

◽

AIRONG WEI ◽

POOM KUMAM ◽

◽

...

Keyword(s):

Fixed Point ◽

Equilibrium Problems ◽

Reflexive Banach Space ◽

Projection Methods ◽

Fixed Point Problem ◽

Projection Algorithm ◽

Point Problem ◽

Bregman Projection ◽

Strict Pseudocontraction ◽

Monotone Variational Inequality

The purpose of this article is to investigate a projection algorithm for solving a fixed point problem of a closed multi-valued Bregman quasi-strict pseudocontraction and an equilibrium problem of a bifunction. Strong convergence of the projection algorithm is obtained without any compact assumption in a reflexive Banach space. As applications, monotone variational inequality problems are considered. Finally, a numerical simulation example is presented for demonstrating the feasibility and convergence of the algorithm proposed in main result.

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Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed-Point Problems, and Variational Inclusions with Application to Minimization Problem

Journal of Applied Mathematics ◽

10.1155/2012/538912 ◽

2012 ◽

Vol 2012 ◽

pp. 1-29 ◽

Cited By ~ 2

Author(s):

Tanom Chamnarnpan ◽

Poom Kumam

Keyword(s):

Fixed Point ◽

Equilibrium Problems ◽

Real Hilbert Space ◽

Nonexpansive Mappings ◽

Monotone Mapping ◽

Iterative Algorithms ◽

Infinite Family ◽

Common Element ◽

Mixed Equilibrium Problems ◽

Mixed Equilibrium

We introduce a new iterative algorithm for solving a common solution of the set of solutions of fixed point for an infinite family of nonexpansive mappings, the set of solution of a system of mixed equilibrium problems, and the set of solutions of the variational inclusion for aβ-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Furthermore, we give a numerical example which supports our main theorem in the last part.

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