Set-valued equilibrium problems with applications to Browder variational inclusions and to fixed point theory

2016 ◽  
Vol 28 ◽  
pp. 251-268 ◽  
Author(s):  
Boualem Alleche ◽  
Vicenţiu D. Rădulescu
Keyword(s):  
Fixed Point ◽  
Equilibrium Problems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Variational Inclusions

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 Stability for a New Class of GNOVI with (γG,λ)-Weak-GRD Mappings in Positive Hilbert Spaces

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Hong Gang Li ◽  
Yongqin Yang ◽  
Mao Ming Jin ◽  
Qinghua Zhang
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Variational Inclusions ◽  
New Class ◽  
Set Up ◽  
The Stability

By using ordered fixed point theory, we set up a new class of GNOVI structures (general nonlinear ordered variational inclusions) with(γG,λ)-weak-GRD mappings, discuss an existence theorem of solution, consider a perturbed Ishikawa iterative algorithm and the convergence of iterative sequences generated by the algorithm, and show the stability of algorithm for GNOVI structures in positive Hilbert spaces. The results in the instrument are obtained.

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.

Modeling the dynamics of hepatitis E via the Caputo–Fabrizio derivative

2019 ◽  
Vol 14 (3) ◽  
pp. 311 ◽  
Author(s):  
Muhammad Altaf Khan ◽  
Zakia Hammouch ◽  
Dumitru Baleanu
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Numerical Scheme ◽  
Arbitrary Order ◽  
Fixed Point Theory ◽  
Hepatitis E ◽  
Point Theory ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Essential Properties

A virus that causes hepatitis E is known as (HEV) and regarded on of the reason for lever inflammation. In mathematical aspects a very low attention has been paid to HEV dynamics. Therefore, the present work explores the HEV dynamics in fractional derivative. The Caputo–Fabriizo derivative is used to study the dynamics of HEV. First, the essential properties of the model will be presented and then describe the HEV model with CF derivative. Application of fixed point theory is used to obtain the existence and uniqueness results associated to the model. By using Adams–Bashfirth numerical scheme the solution is obtained. Some numerical results and tables for arbitrary order derivative are presented.

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