scholarly journals Difference gap functions and global error bounds for random mixed equilibrium problems

Filomat ◽  
2020 ◽  
Vol 34 (8) ◽  
pp. 2739-2761
Author(s):  
Nguyen Hung ◽  
Xiaolong Qin ◽  
Vo Tam ◽  
Jen-Chih Yao
Keyword(s):  
Hilbert Spaces ◽  
Error Bounds ◽  
Equilibrium Problems ◽  
Gap Function ◽  
Global Error ◽  
Gap Functions ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium ◽  
The Difference ◽  
Regularized Gap Functions

The aim of this paper is to study the difference gap (in short, D-gap) function and error bounds for a class of the random mixed equilibrium problems in real Hilbert spaces. Firstly, we consider regularized gap functions of the Fukushima type and Moreau-Yosida type. Then difference gap functions are established by using these terms of regularized gap functions. Finally, the global error bounds for random mixed equilibrium problems are also developed. The results obtained in this paper are new and extend some corresponding known results in literatures. Some examples are given for the illustration of our 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.

scholarly journals Shrinking Projection Method of Common Fixed Point Problems for Discrete Asymptotically Strictly Pseudocontractive Semigroups and Mixed Equilibrium Problems in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-17
Author(s):  
Pattanapong Tianchai
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Shrinking Projection Method ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

This paper is concerned with a common element of the set of common fixed point for a discrete asymptotically strictly pseudocontractive semigroup and the set of solutions of the mixed equilibrium problems in Hilbert spaces. The strong convergence theorem for the above two sets is obtained by a general iterative scheme based on the shrinking projection method which extends and improves the corresponding ones due to Kim [Proceedings of the Asian Conference on Nonlinear Analysis and Optimization (Matsue, Japan, 2008), 139–162].

scholarly journals Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone

2021 ◽  
Author(s):  
Nguyen Van Hung ◽  
Vicente Novo ◽  
Vo Minh Tam
Keyword(s):  
Partial Order ◽  
Error Bounds ◽  
Equilibrium Problems ◽  
Polyhedral Cone ◽  
Gap Functions ◽  
Vector Equilibrium Problems ◽  
Error Bound Analysis ◽  
Vector Equilibrium ◽  
Vector Valued Function ◽  
Regularized Gap Functions

AbstractThe aim of this paper is to establish new results on the error bounds for a class of vector equilibrium problems with partial order provided by a polyhedral cone generated by some matrix. We first propose some regularized gap functions of this problem using the concept of $$\mathcal {G}_{A}$$ G A -convexity of a vector-valued function. Then, we derive error bounds for vector equilibrium problems with partial order given by a polyhedral cone in terms of regularized gap functions under some suitable conditions. Finally, a real-world application to a vector network equilibrium problem is given to illustrate the derived theoretical results.

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