STRONG CONVERGENCE THEOREM FOR A GENERALIZED EQUILIBRIUM PROBLEM AND A PSEUDOCONTRACTIVE MAPPING IN A HILBERT SPACE

Taiwanese Journal of Mathematics ◽

10.11650/twjm/1500406022 ◽

2010 ◽

Vol 14 (5) ◽

pp. 1881-1901 ◽

Author(s):

Lu-Chuan Ceng ◽

Adrian Petrusel ◽

Mu-Ming Wong

Keyword(s):

Hilbert Space ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Strong Convergence Theorem ◽

Generalized Equilibrium Problem ◽

Pseudocontractive Mapping ◽

Generalized Equilibrium

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Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space

Nonlinear Analysis ◽

10.1016/j.na.2008.02.042 ◽

2008 ◽

Vol 69 (3) ◽

pp. 1025-1033 ◽

Author(s):

Satoru Takahashi ◽

Wataru Takahashi

Keyword(s):

Hilbert Space ◽

Nonexpansive Mapping ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Strong Convergence Theorem ◽

Generalized Equilibrium Problem ◽

Generalized Equilibrium

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Strong Convergence Theorem for a Generalized Equilibrium Problem and a Family of Infinitely Quasi(φ)-Nonexpansive Mappings in a Banach Space

Acta Analysis Functionalis Applicata ◽

10.3724/sp.j.1160.2013.00253 ◽

2013 ◽

Vol 15 (3) ◽

pp. 253

Author(s):

Dezhou KONG

Keyword(s):

Banach Space ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Nonexpansive Mappings ◽

Strong Convergence Theorem ◽

Generalized Equilibrium Problem ◽

Generalized Equilibrium

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Strong convergence theorem for a generalized equilibrium problem and system of variational inequalities problem and infinite family of strict pseudo-contractions

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2011-23 ◽

2011 ◽

Vol 2011 (1) ◽

Author(s):

Atid Kangtunyakarn

Keyword(s):

Variational Inequalities ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Infinite Family ◽

Strong Convergence Theorem ◽

Generalized Equilibrium Problem ◽

System Of Variational Inequalities ◽

Generalized Equilibrium

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Strong convergence theorem for a generalized equilibrium problem and a k-strict pseudocontraction in Hilbert spaces

Applied Mathematics and Mechanics ◽

10.1007/s10483-009-0602-z ◽

2009 ◽

Vol 30 (6) ◽

pp. 685-694 ◽

Author(s):

Shi-sheng Zhang ◽

Ruo-feng Rao ◽

Jia-lin Huang

Keyword(s):

Strong Convergence ◽

Equilibrium Problem ◽

Hilbert Spaces ◽

Convergence Theorem ◽

Strong Convergence Theorem ◽

Generalized Equilibrium Problem ◽

Strict Pseudocontraction ◽

Generalized Equilibrium

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Strong convergence theorem for the modified generalized equilibrium problem and fixed point problem of strictly pseudo-contractive mappings

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2014-86 ◽

2014 ◽

Vol 2014 (1) ◽

Author(s):

Sarawut Suwannaut ◽

Atid Kangtunyakarn

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Fixed Point Problem ◽

Strong Convergence Theorem ◽

Point Problem ◽

Generalized Equilibrium Problem ◽

Contractive Mappings ◽

Generalized Equilibrium

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Strong Convergence Theorem for a Generalized Equilibrium Problem with Perturbed Mapping and a Fixed Point Problem of k-Strict Pseudocontraction

Acta Analysis Functionalis Applicata ◽

10.3724/sp.j.1160.2012.00282 ◽

2012 ◽

Vol 14 (3) ◽

pp. 282

Author(s):

Huiying HU ◽

Liuchuan ZENG

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Equilibrium Problem ◽

Convergence Theorem ◽

Fixed Point Problem ◽

Strong Convergence Theorem ◽

Point Problem ◽

Generalized Equilibrium Problem ◽

Strict Pseudocontraction ◽

Generalized Equilibrium

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Strong Convergence Theorems for a Generalized Equilibrium Problem with a Relaxed Monotone Mapping and a Countable Family of Nonexpansive Mappings in a Hilbert Space

Fixed Point Theory and Applications ◽

10.1155/2010/230304 ◽

2010 ◽

Vol 2010 ◽

pp. 1-23 ◽

Author(s):

Shenghua Wang ◽

Giuseppe Marino ◽

Fuhai Wang

Keyword(s):

Hilbert Space ◽

Strong Convergence ◽

Equilibrium Problem ◽

Nonexpansive Mappings ◽

Monotone Mapping ◽

Countable Family ◽

Generalized Equilibrium Problem ◽

Convergence Theorems ◽

Generalized Equilibrium

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Strong convergence of the viscosity approximation method for the split generalized equilibrium problem

Rendiconti del Circolo Matematico di Palermo (1952 -) ◽

10.1007/s12215-021-00617-7 ◽

2021 ◽

Author(s):

Withun Phuengrattana ◽

Chalongchai Klanarong

Keyword(s):

Strong Convergence ◽

Equilibrium Problem ◽

Approximation Method ◽

Viscosity Approximation Method ◽

Generalized Equilibrium Problem ◽

Viscosity Approximation ◽

Generalized Equilibrium ◽

Split Generalized Equilibrium Problem

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A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

Fixed Point Theory and Applications ◽

10.1186/1687-1812-2011-17 ◽

2011 ◽

Vol 2011 (1) ◽

Author(s):

De-ning Qu ◽

Cao-zong Cheng

Keyword(s):

Banach Space ◽

Fixed Point ◽

Strong Convergence ◽

Convergence Theorem ◽

Equilibrium Problems ◽

Fixed Point Problems ◽

Strong Convergence Theorem ◽

Generalized Equilibrium

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Iterative approximations with hybrid techniques for fixed points and equilibrium problems

Filomat ◽

10.2298/fil1607997a ◽

2016 ◽

Vol 30 (7) ◽

pp. 1997-2009

Author(s):

Afrah Abdou ◽

Badriah Alamri ◽

Yeol Cho ◽

Li-Jun Zhu

Keyword(s):

Fixed Point ◽

Strong Convergence ◽

Convergence Theorem ◽

Equilibrium Problems ◽

Fixed Point Problem ◽

Strong Convergence Theorem ◽

Point Problem ◽

Hybrid Techniques ◽

Contractive Mappings ◽

Generalized Equilibrium

In this paper, we consider an iterative algorithm by using the shrinking projection method for solving the fixed point problem of the pseudo-contractive mappings and the generalized equilibrium problems. We prove some lemmas for our main result and a strong convergence theorem for the proposed algorithm.

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