RELAXED EXTRAGRADIENT-LIKE METHOD FOR GENERAL SYSTEM OF GENERALIZED MIXED EQUILIBRIA AND FIXED POINT PROBLEM

In this paper, we introduce two iterative algorithms based on the relaxed extragradient-like method for finding a common element of the solution set of a general system of generalized mixed equilibria and the fixed point set of a strictly pseudocontractive mapping in a real Hilbert space. We will pr...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 16; no. 2; pp. 445 - 478
Main Authors Ceng, Lu-Chuan, Petruşel, Adrian
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.04.2012
Subjects
Mathematical problems
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Summary:In this paper, we introduce two iterative algorithms based on the relaxed extragradient-like method for finding a common element of the solution set of a general system of generalized mixed equilibria and the fixed point set of a strictly pseudocontractive mapping in a real Hilbert space. We will prove the weak convergence of the iterative algorithm under some mild conditions, while the strong convergence is obtained under some more restrictive conditions. 2010Mathematics Subject Classification: 49J30, 49J40, 47J25, 47H09. Key words and phrases: Strictly pseudocontractive mapping, Fixed point, Inverse strongly monotone mapping, Relaxed extragradient-like method, General system of generalized mixed equilibria.
ISSN:1027-5487
2224-6851
DOI:10.11650/twjm/1500406595