Strong Convergence of a Projection-Type Method for Mixed Variational Inequalities in Hilbert Spaces

2018 ◽  
Vol 39 (11) ◽  
pp. 1103-1119 ◽  
Author(s):  
Guo-ji Tang ◽  
Zhongping Wan ◽  
Nan-jing Huang
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Type Method ◽  
Mixed Variational Inequalities

scholarly journals A General Inertial Viscosity Type Method for Nonexpansive Mappings and Its Applications in Signal Processing

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 288 ◽  
Author(s):  
Yinglin Luo ◽  
Meijuan Shang ◽  
Bing Tan
Keyword(s):  
Signal Processing ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Type Method ◽  
Pseudocontractive Mappings ◽  
Inertia Parameters ◽  
Strictly Pseudocontractive Mappings

In this paper, we propose viscosity algorithms with two different inertia parameters for solving fixed points of nonexpansive and strictly pseudocontractive mappings. Strong convergence theorems are obtained in Hilbert spaces and the applications to the signal processing are considered. Moreover, some numerical experiments of proposed algorithms and comparisons with existing algorithms are given to the demonstration of the efficiency of the proposed algorithms. The numerical results show that our algorithms are superior to some related algorithms.

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 a Unified General Iteration fork-Strictly Pseudononspreading Mapping in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Dao-Jun Wen ◽  
Yi-An Chen ◽  
Yan Tang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Minimization Problem ◽  
Iterative Sequence ◽  
Mean Convergence ◽  
Strictly Pseudononspreading Mapping ◽  
General Iterative Method

We introduce a unified general iterative method to approximate a fixed point ofk-strictly pseudononspreading mapping. Under some suitable conditions, we prove that the iterative sequence generated by the proposed method converges strongly to a fixed point of ak-strictly pseudononspreading mapping with an idea of mean convergence, which also solves a class of variational inequalities as an optimality condition for a minimization problem. The results presented in this paper may be viewed as a refinement and as important generalizations of the previously known results announced by many other authors.

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