Strong convergence theorem by a new hybrid method for equilibrium problems and variational inequality problems

2010 ◽  
Vol 72 (2) ◽  
pp. 847-855 ◽  
Author(s):  
Li HongYu ◽  
Su YongFu
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem

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.

A new self adaptive Tseng’s extragradient method with double-projection for solving pseudomonotone variational inequality problems in Hilbert spaces

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhongbing Xie ◽  
Gang Cai ◽  
Xiaoxiao Li ◽  
Qiao-Li Dong
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Extragradient Method ◽  
Variational Inequality Problems ◽  
Strong Convergence Theorem ◽  
Tseng’S Extragradient Method

Abstract The purpose of this paper is to study a new Tseng’s extragradient method with two different stepsize rules for solving pseudomonotone variational inequalities in real Hilbert spaces. We prove a strong convergence theorem of the proposed algorithm under some suitable conditions imposed on the parameters. Moreover, we also give some numerical experiments to demonstrate the performance of our algorithm.

scholarly journals An Alternative Regularization Method for Equilibrium Problems and Fixed Point of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Shuo Sun
Keyword(s):  
Fixed Point ◽  
Variational Inequality ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Convergence Theorem ◽  
Regularization Method ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Sunny Nonexpansive Retraction

We introduce a new regularization iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping. Then, we prove a strong convergence theorem for nonexpansive mappings to solve a unique solution of the variational inequality and the unique sunny nonexpansive retraction. Our results extend beyond the results of S. Takahashi and W. Takahashi (2007), and many others.

scholarly journals Strong Convergence Theorem for Bregman Strongly Nonexpansive Mappings and Equilibrium Problems in Reflexive Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinhua Zhu ◽  
Shih-sen Chang ◽  
Min Liu
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Reflexive Banach Space ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Strong Convergence Theorem ◽  
Reflexive Banach Spaces

By using a new hybrid method, a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of Bregman strongly nonexpansive mappings in a reflexive Banach space is proved.

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