A Modified Krasnosel’skiǐ–Mann Iterative Algorithm for Approximating Fixed Points of Enriched Nonexpansive Mappings

For approximating the fixed points of enriched nonexpansive mappings in Hilbert spaces, we consider a modified Krasnosel’skiǐ–Mann algorithm for which we prove a strong convergence theorem. We also empirically compare the rate of convergence of the modified Krasnosel’skiǐ–Mann algorithm and of the simple Krasnosel’skiǐ fixed point algorithm. Based on the numerical experiments reported in the paper we conclude that, for the class of enriched nonexpansive mappings, it is more convenient to work with the simple Krasnosel’skiǐ fixed point algorithm than with the modified Krasnosel’skiǐ–Mann algorithm.

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Modified CQ-Algorithms for G-Nonexpansive Mappings in Hilbert Spaces Involving Graphs

New Mathematics and Natural Computation ◽

10.1142/s1793005720500064 ◽

2020 ◽

Vol 16 (01) ◽

pp. 89-103

Author(s):

W. Cholamjiak ◽

D. Yambangwai ◽

H. Dutta ◽

H. A. Hammad

Keyword(s):

Hilbert Space ◽

Fixed Point ◽

Strong Convergence ◽

Common Fixed Point ◽

Rate Of Convergence ◽

Hilbert Spaces ◽

Numerical Experiments ◽

Nonexpansive Mappings ◽

Iterative Schemes ◽

Cq Method

In this paper, we introduce four new iterative schemes by modifying the CQ-method with Ishikawa and [Formula: see text]-iterations. The strong convergence theorems are given by the CQ-projection method with our modified iterations for obtaining a common fixed point of two [Formula: see text]-nonexpansive mappings in a Hilbert space with a directed graph. Finally, to compare the rate of convergence and support our main theorems, we give some numerical experiments.

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A Strong Convergence Theorem for a Common Fixed Point of Two Sequences of Strictly Pseudocontractive Mappings in Hilbert Spaces and Applications

Abstract and Applied Analysis ◽

10.1155/2010/876819 ◽

2010 ◽

Vol 2010 ◽

pp. 1-17 ◽

Cited By ~ 2

Author(s):

Kasamsuk Ungchittrakool

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Common Fixed Point ◽

Hilbert Spaces ◽

Convergence Theorem ◽

Common Element ◽

Strong Convergence Theorem ◽

Pseudocontractive Mappings ◽

Strict Pseudocontraction ◽

Strictly Pseudocontractive Mappings

We prove a strong convergence theorem for a common fixed point of two sequences of strictly pseudocontractive mappings in Hilbert spaces. We also provide some applications of the main theorem to find a common element of the set of fixed points of a strict pseudocontraction and the set of solutions of an equilibrium problem in Hilbert spaces. The results extend and improve the recent ones announced by Marino and Xu (2007) and others.

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Convergence theorems for Bregman strongly nonexpansive mappings in reflexive Banach spaces

Filomat ◽

10.2298/fil1407525z ◽

2014 ◽

Vol 28 (7) ◽

pp. 1525-1536 ◽

Cited By ~ 6

Author(s):

Habtu Zegeye

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Common Fixed Point ◽

Banach Spaces ◽

Convergence Theorem ◽

Nonexpansive Mappings ◽

Finite Family ◽

Strong Convergence Theorem ◽

Monotone Mappings ◽

Convergence Theorems

In this paper, we study a strong convergence theorem for a common fixed point of a finite family of Bregman strongly nonexpansive mappings in the framework of reflexive real Banach spaces. As a consequence, we prove convergence theorem for a common fixed point of a finite family of Bergman relatively nonexpansive mappings. Furthermore, we apply our method to prove strong convergence theorems of iterative algorithms for finding a common zero of a finite family of Bregman inverse strongly monotone mappings and a solution of a finite family of variational inequality problems.

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

Mathematics ◽

10.3390/math8020288 ◽

2020 ◽

Vol 8 (2) ◽

pp. 288 ◽

Cited By ~ 1

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.

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

International Journal of Nonlinear Sciences and Numerical Simulation ◽

10.1515/ijnsns-2021-0028 ◽

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.

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