scholarly journals Strong convergent iterative techniques for 2-generalized hybrid mappings and split equilibrium problems

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 5851-5862
Author(s):  
Jing Zhao ◽  
Yunshui Liang ◽  
Zhenhai Liu
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Split Equilibrium Problem ◽  
Iterative Techniques ◽  
Numerical Example ◽  
Common Solution

In this paper, we suggest a new iterative scheme for finding a common element of the set of solutions of a split equilibrium problem and the set of fixed points of 2-generalized hybrid mappings in Hilbert spaces. We show that the iteration converges strongly to a common solution of the considered problems. A numerical example is illustrated to verify the validity of the proposed algorithm. The results obtained in this paper extend and improve some known results in the literature.

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 Results of Split Equilibrium Problems and Fixed Point Problems

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Li-Jun Zhu ◽  
Hsun-Chih Kuo ◽  
Ching-Feng Wen
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Convergence Results

In this paper, we investigate the split equilibrium problem and fixed point problem in Hilbert spaces. We propose an iterative scheme for solving such problem in which the involved equilibrium bifunctions f and g are pseudomonotone and monotone, respectively, and the operators S and T are all pseudocontractive. We show that the suggested scheme converges strongly to a solution of the considered problem.

scholarly journals Viscosity Approximations by the Shrinking Projection Method of Quasi-Nonexpansive Mappings for Generalized Equilibrium Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-30 ◽  
Author(s):  
Rabian Wangkeeree ◽  
Nimit Nimana
Keyword(s):  
Fixed Points ◽  
Equilibrium Problem ◽  
Projection Method ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Generalized Equilibrium Problem ◽  
Shrinking Projection Method ◽  
Generalized Equilibrium

We introduce viscosity approximations by using the shrinking projection method established by Takahashi, Takeuchi, and Kubota, for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of a quasi-nonexpansive mapping. Furthermore, we also consider the viscosity shrinking projection method for finding a common element of the set of solutions of the generalized equilibrium problem and the set of fixed points of the super hybrid mappings in Hilbert spaces.

scholarly journals Convergence analysis for combination of equilibrium problems and k-nonspreading multi-valued mappings

2021 ◽  
Author(s):  
Suhel Ahmad Khan ◽  
Kaleem Raza Kazmi ◽  
Watcharaporn Cholamjiak ◽  
Hemen Dutta
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Convergence Analysis ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Solution Set ◽  
Strong Convergence Theorem ◽  
Numerical Example ◽  
Common Solution

We prove a strong convergence theorem for finding a common solution of a combination of equilibrium problems and the set of fixed points of a k-nonspreading multi-valued mapping by using shrinking projection hybrid method. Further, we give a numerical example to justify our main result and compare the shrinking areas of solution set after randomization.

scholarly journals Approximate Equilibrium Problems and Fixed Points

2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
H. Mazaheri ◽  
S. A. M. Mohsenalhosseini
Keyword(s):  
Hilbert Space ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Common Element ◽  
Approximate Equilibrium

We find a common element of the set of fixed points of a map and the set of solutions of an approximate equilibrium problem in a Hilbert space. Then, we show that one of the sequences weakly converges. Also we obtain some theorems about equilibrium problems and fixed points.

scholarly journals Convergence Theorems for Equilibrium Problems and Fixed-Point Problems of an Infinite Family ofki-Strictly Pseudocontractive Mapping in Hilbert Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-23
Author(s):  
Haitao Che ◽  
Meixia Li ◽  
Xintian Pan
Keyword(s):  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Infinite Family ◽  
Common Element ◽  
Strictly Pseudocontractive Mapping ◽  
Pseudocontractive Mappings ◽  
Definition Of ◽  
Strictly Pseudocontractive Mappings

We first extend the definition of Wnfrom an infinite family of nonexpansive mappings to an infinite family of strictly pseudocontractive mappings, and then propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of an infinite family ofki-strictly pseudocontractive mappings in Hilbert spaces. The results obtained in this paper extend and improve the recent ones announced by many others. Furthermore, a numerical example is presented to illustrate the effectiveness of the proposed scheme.

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.

scholarly journals Approximation results for split equilibrium problems and fixed point problems of nonexpansive semigroup in Hilbert spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Yasir Arfat ◽  
Poom Kumam ◽  
Parinya Sa Ngiamsunthorn ◽  
Muhammad Aqeel Ahmad Khan ◽  
Hammad Sarwar ◽  
...  
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Extragradient Method ◽  
Fixed Point Problem ◽  
Nonexpansive Semigroup ◽  
Point Problem ◽  
Split Equilibrium Problem ◽  
Common Solution ◽  
Theoretical Results

Abstract In this paper, we study a modified extragradient method for computing a common solution to the split equilibrium problem and fixed point problem of a nonexpansive semigroup in real Hilbert spaces. The weak and strong convergence characteristics of the proposed algorithm are investigated by employing suitable control conditions in such a setting of spaces. As a consequence, we provide a simplified analysis of various existing results concerning the extragradient method in the current literature. We also provide a numerical example to strengthen the theoretical results and the applicability of the proposed algorithm.

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