scholarly journals A new iterative algorithm of pseudomonotone mappings for equilibrium problems in Hilbert spaces

2013 ◽  
Vol 2013 (1) ◽  
Author(s):  
Jong Kyu Kim ◽  
Won Hee Lim
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Pseudomonotone Mappings

scholarly journals Projected Subgradient Algorithms for Pseudomonotone Equilibrium Problems and Fixed Points of Pseudocontractive Operators

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 461 ◽  
Author(s):  
Yonghong Yao ◽  
Naseer Shahzad ◽  
Jen-Chih Yao
Keyword(s):  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Convergence Result ◽  
Subgradient Method ◽  
Iterative Sequence ◽  
Common Element ◽  
Lipschitz Continuous ◽  
Subgradient Algorithms ◽  
Continuous Operators

The projected subgradient algorithms can be considered as an improvement of the projected algorithms and the subgradient algorithms for the equilibrium problems of the class of monotone and Lipschitz continuous operators. In this paper, we present and analyze an iterative algorithm for finding a common element of the fixed point of pseudocontractive operators and the pseudomonotone equilibrium problem in Hilbert spaces. The suggested iterative algorithm is based on the projected method and subgradient method with a linearsearch technique. We show the strong convergence result for the iterative sequence generated by this algorithm. Some applications are also included. Our result improves and extends some existing results in the literature.

scholarly journals Construction of a common element for the set of solutions of fixed point problems and generalized equilibrium problems in Hilbert spaces

2016 ◽  
Vol 15 (1) ◽  
pp. 79-96
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Iterative Algorithm ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Finite Family ◽  
Common Element ◽  
Common Solution ◽  
Convergence Results ◽  
Generalized Equilibrium

AbstractIn this paper, we propose and analyse an iterative algorithm for the approximation of a common solution for a finite family of k-strict pseudocontractions and two finite families of generalized equilibrium problems in the setting of Hilbert spaces. Strong convergence results of the proposed iterative algorithm together with some applications to solve the variational inequality problems are established in such setting. Our results generalize and improve various existing results in the current literature.

scholarly journals An iterative algorithm for the system of split mixed equilibrium problem

2020 ◽  
Vol 53 (1) ◽  
pp. 309-324
Author(s):  
Ibrahim Karahan ◽  
Lateef Olakunle Jolaoso
Keyword(s):  
Variational Inequality ◽  
Iterative Algorithm ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Equilibrium System ◽  
Convergence Conditions ◽  
Mixed Equilibrium Problems ◽  
Split Variational Inequality ◽  
Mixed Equilibrium ◽  
Split Mixed Equilibrium Problem

AbstractIn this article, a new problem that is called system of split mixed equilibrium problems is introduced. This problem is more general than many other equilibrium problems such as problems of system of equilibrium, system of split equilibrium, split mixed equilibrium, and system of split variational inequality. A new iterative algorithm is proposed, and it is shown that it satisfies the weak convergence conditions for nonexpansive mappings in real Hilbert spaces. Also, an application to system of split variational inequality problems and a numeric example are given to show the efficiency of the results. Finally, we compare its rate of convergence other algorithms and show that the proposed method converges faster.

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