scholarly journals Алгоритм нелинейной вязкости с возмущением для нерасширяющих многозначных отображений

2021 ◽  
pp. 60-76
Author(s):  
H.R. Sahebi
Keyword(s):  
Linear Programming ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Common Element ◽  
Nonlinear Operators ◽  
Numerical Examples ◽  
Nonlinear Viscosity

The viscosity iterative algorithms for finding a common element of the set of fixed points for nonlinear operators and the set of solutions of variational inequality problems have been investigated by many authors. The viscosity technique allow us to apply this method to convex optimization, linear programming and monoton inclusions. In this paper, based on viscosity technique with perturbation, we introduce a new nonlinear viscosity algorithm for finding an element of~the set of~fixed points of nonexpansive multi-valued mappings in a Hilbert spaces. Furthermore, strong convergence theorems of~this algorithm were established under suitable assumptions imposed on~parameters. Our results can be viewed as a generalization and improvement of various existing results in the current literature. Moreover, some numerical examples that show the efficiency and implementation of our algorithm are presented.

scholarly journals New Hybrid Steepest Descent Algorithms for Equilibrium Problem and Infinitely Many Strict Pseudo-Contractions in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Peichao Duan
Keyword(s):  
Variational Inequality ◽  
Iterative Method ◽  
Strong Convergence ◽  
Equilibrium Problem ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Common Element ◽  
Numerical Examples ◽  
Contractive Mappings ◽  
General Iterative Method

We propose an explicit iterative scheme for finding a common element of the set of fixed points of infinitely many strict pseudo-contractive mappings and the set of solutions of an equilibrium problem by the general iterative method, which solves the variational inequality. In the setting of real Hilbert spaces, strong convergence theorems are proved. The results presented in this paper improve and extend the corresponding results reported by some authors recently. Furthermore, two numerical examples are given to demonstrate the effectiveness of our iterative scheme.

scholarly journals S-iteration process of Halpern-type for common solutions of nonexpansive mappings and monotone variational inequalities

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1727-1746 ◽  
Author(s):  
D.R. Sahu ◽  
Ajeet Kumar ◽  
Ching-Feng Wen
Keyword(s):  
Variational Inequality ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Common Element ◽  
Monotone Mappings ◽  
Monotone Variational Inequalities ◽  
Numerical Examples ◽  
Inverse Strongly Monotone ◽  
Strongly Monotone Mappings

This paper is devoted to the strong convergence of the S-iteration process of Halpern-type for approximating a common element of the set of fixed points of a nonexpansive mapping and the set of common solutions of variational inequality problems formed by two inverse strongly monotone mappings in the framework of Hilbert spaces. We also give some numerical examples in support of our main result.

scholarly journals Tikhonov Regularization Terms for Accelerating Inertial Mann-Like Algorithm with Applications

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 554
Author(s):  
Hasanen A. Hammad ◽  
Habib ur Rehman ◽  
Hassan Almusawa
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Fixed Points ◽  
Tikhonov Regularization ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Nonexpansive Mappings ◽  
Inclusion Problem ◽  
Monotone Inclusion ◽  
Monotone Inclusion Problem

In this manuscript, we accelerate the modified inertial Mann-like algorithm by involving Tikhonov regularization terms. Strong convergence for fixed points of nonexpansive mappings in real Hilbert spaces was discussed utilizing the proposed algorithm. Accordingly, the strong convergence of a forward–backward algorithm involving Tikhonov regularization terms was derived, which counts as finding a solution to the monotone inclusion problem and the variational inequality problem. Ultimately, some numerical discussions are presented here to illustrate the effectiveness of our algorithm.

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).

Strong and weak convergence theorems for general mixed equilibrium problems and general variational inequality problems and fixed point problems for two nonexpansive semigroups in Hilbert spaces

2021 ◽  
pp. 152-160
Author(s):  
Baoshuai Zhang ◽  
◽  
Ying Tian ◽  
Keyword(s):  
Variational Inequality ◽  
Weak Convergence ◽  
Hilbert Spaces ◽  
Iterative Algorithms ◽  
Common Element ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Nonexpansive Semigroups ◽  
General Variational Inequality ◽  
Mixed Equilibrium

In this paper, we introduce some iterative algorithms for finding a common element of the set of solutions of the general mixed equilibrium problem and the set of solutions of a general variational inequality for two cocoercive mappings and the set of common fixed points of two nonexpansive semigroups in Hilbert space. We obtain both strong and weak convergence theorems for the sequences generated by these iterative processes in Hilbert spaces. Our results improve and extend the results announced by many others.

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 A Generalized Strong Convergence Algorithm in the Presence of Errors for Variational Inequality Problems in Hilbert Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Mostafa Ghadampour ◽  
Donal O’Regan ◽  
Ebrahim Soori ◽  
Ravi P. Agarwal
Keyword(s):  
Variational Inequality ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Variational Inequality Problem ◽  
Numerical Algorithms ◽  
Variational Inequality Problems ◽  
Numerical Examples ◽  
Inequality Problem ◽  
Convergence Of An Algorithm ◽  
Computational Errors

In this paper, we study the strong convergence of an algorithm to solve the variational inequality problem which extends a recent paper (Thong et al., Numerical Algorithms. 78, 1045-1060 (2018)). We reduce and refine some of their algorithm conditions and we prove the convergence of the algorithm in the presence of some computational errors. Then, using the MATLAB software, the result will be illustrated with some numerical examples. Also, we compare our algorithm with some other well-known algorithms.

scholarly journals Convergence Theorem for Equilibrium and Variational Inequality Problems and a Family of Infinitely Nonexpansive Mappings in Hilbert Space

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Zhou Yinying ◽  
Cao Jiantao ◽  
Wang Yali
Keyword(s):  
Hilbert Space ◽  
Variational Inequality ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problem ◽  
Convergence Theorem ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Common Element

We introduce a hybrid iterative scheme for finding a common element of the set of common fixed points for a family of infinitely nonexpansive mappings, the set of solutions of the varitional inequality problem and the equilibrium problem in Hilbert space. Under suitable conditions, some strong convergence theorems are obtained. Our results improve and extend the corresponding results in (Chang et al. (2009), Min and Chang (2012), Plubtieng and Punpaeng (2007), S. Takahashi and W. Takahashi (2007), Tada and Takahashi (2007), Gang and Changsong (2009), Ying (2013), Y. Yao and J. C. Yao (2007), and Yong-Cho and Kang (2012)).

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