Quasi-Equilibrium Problems and Fixed Point Theorems of Separately l.s.c and u.s.c Mappings

2017 ◽  
Vol 39 (2) ◽  
pp. 233-255 ◽  
Author(s):  
Nguyen Xuan Tan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Quasi Equilibrium

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

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.

scholarly journals Order-clustered fixed point theorems and their applications to Pareto equilibrium problems

2017 ◽  
Vol 18 (2) ◽  
pp. 755-772 ◽  
Author(s):  
Linsen Xie ◽  
◽  
Jinlu Li ◽  
Adrian Petrușel ◽  
Jen-Chih Yao ◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Pareto Equilibrium

scholarly journals New extragradient methods with non-convex combination for pseudomonotone equilibrium problems with applications in Hilbert spaces

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1677-1693 ◽  
Author(s):  
Shenghua Wang ◽  
Yifan Zhang ◽  
Ping Ping ◽  
Yeol Cho ◽  
Haichao Guo
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Convex Combination ◽  
Projection Methods ◽  
Extragradient Methods ◽  
Numerical Examples

In the literature, the most authors modify the viscosity methods or hybrid projection methods to construct the strong convergence algorithms for solving the pseudomonotone equilibrium problems. In this paper, we introduce some new extragradient methods with non-convex combination to solve the pseudomonotone equilibrium problems in Hilbert space and prove the strong convergence for the constructed algorithms. Our algorithms are very different with the existing ones in the literatures. As the application, the fixed point theorems for strict pseudo-contraction are considered. Finally, some numerical examples are given to show the effectiveness of the algorithms.

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