Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory

2008 ◽  
Vol 69 (1) ◽  
pp. 126-139 ◽  
Author(s):  
S. Al-Homidan ◽  
Q.H. Ansari ◽  
J.-C. Yao
Keyword(s):  
Fixed Point ◽  
Variational Principle ◽  
Equilibrium Problems ◽  
Fixed Point Theory ◽  
Point Theory

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

2013 ◽  
Vol 2013 ◽  
pp. 1-1 ◽  
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

scholarly journals About Applications of the Fixed Point Theory

2017 ◽  
Vol 22 (1) ◽  
pp. 13-17
Author(s):  
Amelia Bucur
Keyword(s):  
Fixed Point ◽  
Mathematical Modelling ◽  
Dynamic Systems ◽  
Equilibrium Problems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Dynamic Systems Theory ◽  
Mathematical Economics ◽  
Differential Equations And Inclusions ◽  
Applied Fields

Abstract The fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.

scholarly journals Equilibrium problems and fixed point theory

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Qamrul Hasan Ansari ◽  
Suliman Al-Homidan ◽  
Jen-Chih Yao
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Fixed Point Theory ◽  
Point Theory

scholarly journals MONOTONE AND PSEUDO-MONOTONE EQUILIBRIUM PROBLEMS IN HADAMARD SPACES

2019 ◽  
pp. 1-23 ◽  
Author(s):  
HADI KHATIBZADEH ◽  
VAHID MOHEBBI
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Equilibrium Point ◽  
Proximal Point Algorithm ◽  
Equilibrium Problems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Proximal Point ◽  
Monotone Bifunction ◽  
Monotone Bifunctions

As a continuation of previous work of the first author with Ranjbar [‘A variational inequality in complete CAT(0) spaces’, J. Fixed Point Theory Appl. 17 (2015), 557–574] on a special form of variational inequalities in Hadamard spaces, in this paper we study equilibrium problems in Hadamard spaces, which extend variational inequalities and many other problems in nonlinear analysis. In this paper, first we study the existence of solutions of equilibrium problems associated with pseudo-monotone bifunctions with suitable conditions on the bifunctions in Hadamard spaces. Then, to approximate an equilibrium point, we consider the proximal point algorithm for pseudo-monotone bifunctions. We prove existence of the sequence generated by the algorithm in several cases in Hadamard spaces. Next, we introduce the resolvent of a bifunction in Hadamard spaces. We prove convergence of the resolvent to an equilibrium point. We also prove $\triangle$ -convergence of the sequence generated by the proximal point algorithm to an equilibrium point of the pseudo-monotone bifunction and also the strong convergence under additional assumptions on the bifunction. Finally, we study a regularization of Halpern type and prove the strong convergence of the generated sequence to an equilibrium point without any additional assumption on the pseudo-monotone bifunction. Some examples in fixed point theory and convex minimization are also presented.

Sign in / Sign up

Export Citation Format

Share Document