scholarly journals Extragradient methods with CQ technique for fixed point problems and equilibrium problems

Filomat ◽  
2020 ◽  
Vol 34 (14) ◽  
pp. 4783-4793
Author(s):  
Zhangsong Yao ◽  
Yeong-Cheng Liou ◽  
Li-Jun Zhu
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Algorithms ◽  
Convergence Result ◽  
Fixed Point Problems ◽  
Common Element ◽  
Extragradient Methods ◽  
Extragradient Algorithm

In this paper, we study iterative algorithms for solving fixed point problems and equilibrium problems in Hilbert spaces. We present an extragradient algorithm with CQ technique for finding a common element of the fixed points of pseudocontractive operators and the solutions of pseudomonotone equilibrium problems. Strong convergence result of the proposed algorithm is proved.

scholarly journals Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Shenghua Wang ◽  
Shin Min Kang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Banach Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Iterative Algorithms ◽  
Common Fixed Points ◽  
Common Element ◽  
Fixed Point Set ◽  
Point Set

We first introduce the concept of Bregman asymptotically quasinonexpansive mappings and prove that the fixed point set of this kind of mappings is closed and convex. Then we construct an iterative scheme to find a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a countable family of Bregman asymptotically quasinonexpansive mappings in reflexive Banach spaces and prove strong convergence theorems. Our results extend the recent ones of some others.

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.

scholarly journals Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

scholarly journals General Iterative Methods for Equilibrium Problems and Infinitely Many Strict Pseudocontractions in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Peichao Duan ◽  
Aihong Wang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Iterative Methods ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems ◽  
Pseudocontractive Mappings

We propose an implicit iterative scheme and an explicit iterative scheme for finding a common element of the set of fixed point of infinitely many strict pseudocontractive mappings and the set of solutions of an equilibrium problem by the general iterative methods. In the setting of real Hilbert spaces, strong convergence theorems are proved. Our results improve and extend the corresponding results reported by many others.

scholarly journals Strong Convergence Theorems for Equilibrium Problems andk-Strict Pseudocontractions in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Dao-Jun Wen
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Real Hilbert Space ◽  
Finite Family ◽  
Common Element ◽  
Convergence Theorems

We introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed point of a finite family ofk-strictly pseudo-contractive nonself-mappings. Strong convergence theorems are established in a real Hilbert space under some suitable conditions. Our theorems presented in this paper improve and extend the corresponding results announced by many others.

An Iterative Method for Equilibrium Problems and Fixed Point Problems

2014 ◽  
Vol 513-517 ◽  
pp. 382-385
Author(s):  
Chen Min ◽  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Common Element ◽  
Mixed Equilibrium Problems

In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

scholarly journals Strong convergence inertial projection and contraction method with self adaptive stepsize for pseudomonotone variational inequalities and fixed point problems

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Lateef Olakunle Jolaoso ◽  
Maggie Aphane
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Lipschitz Constant ◽  
Convergence Result ◽  
Common Element ◽  
Adaptive Technique ◽  
Prior Estimate ◽  
Adaptive Stepsize ◽  
Self Adaptive

AbstractIn this paper, we introduce a new inertial self-adaptive projection method for finding a common element in the set of solution of pseudomonotone variational inequality problem and set of fixed point of a pseudocontractive mapping in real Hilbert spaces. The self-adaptive technique ensures the convergence of the algorithm without any prior estimate of the Lipschitz constant. With the aid of Moudafi’s viscosity approximation method, we prove a strong convergence result for the sequence generated by our algorithm under some mild conditions. We also provide some numerical examples to illustrate the accuracy and efficiency of the algorithm by comparing with other recent methods in the literature.

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