Strong convergence theorem by hybrid method for equilibrium problems, variational inequality problems and maximal monotone operators

2010 ◽  
Vol 4 (4) ◽  
pp. 689-698 ◽  
Author(s):  
Qiao-Li Dong ◽  
Bin-Chao Deng
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hybrid Method ◽  
Convergence Theorem ◽  
Equilibrium Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
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 Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

2004 ◽  
Vol 2004 (3) ◽  
pp. 239-249 ◽  
Author(s):  
Fumiaki Kohsaka ◽  
Wataru Takahashi
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Iterative Sequence ◽  
Strong Convergence Theorem ◽  
Convex Minimization Problem ◽  
Proximal Point

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

scholarly journals Split variational inclusions for Bregman multivalued maximal monotone operators

2020 ◽  
Author(s):  
Mujahid Abbas ◽  
Faik Gürsoy ◽  
Yusuf Ibrahim ◽  
Abdul Rahim Khan
Keyword(s):  
Strong Convergence ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Strong Convergence Theorem ◽  
Variational Inclusions ◽  
Uniformly Convex ◽  
Inclusion Problems ◽  
Uniformly Smooth ◽  
Uniformly Smooth Banach Spaces

We introduce a new algorithm to approximate a solution of split variational inclusion problems of multivalued maximal monotone operators in uniformly convex and uniformly smooth Banach spaces under the Bregman distance. A strong convergence theorem for the above problem is established and several important known results are deduced as corollaries to it. As application, we solve a split minimization problem and provide a numerical example to support better findings of our result.

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.

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