Strong Convergence Theorem on Split Equilibrium and Fixed Point Problems in Hilbert Spaces

2016 ◽  
Vol 41 (3) ◽  
pp. 1309-1326 ◽  
Author(s):  
Shenghua Wang ◽  
Xiaoying Gong ◽  
Shinmin Kang
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Fixed Point Problems ◽  
Strong Convergence Theorem

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

2010 ◽  
Vol 2010 ◽  
pp. 1-17 ◽  
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.

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

Symmetry ◽  
2022 ◽  
Vol 14 (1) ◽  
pp. 123
Author(s):  
Vasile Berinde
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Strong Convergence Theorem ◽  
Fixed Point Algorithm ◽  
Mann Algorithm

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.

scholarly journals Strong Convergence by a Hybrid Algorithm for Finding a Common Fixed Point of Lipschitz Pseudocontraction and Strict Pseudocontraction in Hilbert Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Kasamsuk Ungchittrakool
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Hybrid Algorithm ◽  
Strong Convergence Theorem ◽  
Strict Pseudocontraction

We prove a strong convergence theorem by using a hybrid algorithm in order to find a common fixed point of Lipschitz pseudocontraction and κ-strict pseudocontraction in Hilbert spaces. Our results extend the recent ones announced by Yao et al. (2009) and many others.

scholarly journals Viscosity Projection Algorithms for Pseudocontractive Mappings in Hilbert Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xiujuan Pan ◽  
Shin Min Kang ◽  
Young Chel Kwun
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Hilbert Spaces ◽  
Convergence Theorem ◽  
Projection Algorithm ◽  
Strong Convergence Theorem ◽  
Minimum Norm ◽  
Projection Algorithms ◽  
Pseudocontractive Mapping ◽  
Pseudocontractive Mappings

An explicit projection algorithm with viscosity technique is constructed for finding the fixed points of the pseudocontractive mapping in Hilbert spaces. Strong convergence theorem is demonstrated. Consequently, as an application, we can approximate to the minimum-norm fixed point of the pseudocontractive mapping.

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