Taiwanese Journal of Mathematics

A General System of Generalized Nonlinear Mixed Composite-Type Equilibria in Hilbert Spaces

Hui-Ying Hu and Lu-Chuan Ceng

Full-text: Open access

Abstract

Very recently, Ceng and Yao [L. C. Ceng, J. C. Yao, A relaxed extragradient-like method for a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem, Nonlinear Anal., 72 (2009), 1922-1937, suggested and analyzed a relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem, a general system of generalized equilibria and a fixed point problem of a strict pseudocontractive mapping in a Hilbert space. In this paper, based on the authors' iterative method, we introduce a modification of the relaxed extragradient-like method for finding a common solution of a generalized mixed equilibrium problem with perturbed mapping, a general system of generalized nonlinear mixed composite-type equilibria and a fixed point problem of a strict pseudocontractive mapping in a Hilbert space, and then obtain a strong convergence theorem. Utilizing this theorem, we establish some new strong convergence results in fixed point problems, variational inequalities, mixed equilibrium problems and systems of generalized nonlinear mixed composite-type equilibria in Hilbert spaces.

Article information

Source
Taiwanese J. Math., Volume 15, Number 3 (2011), 927-959.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406276

Digital Object Identifier
doi:10.11650/twjm/1500406276

Mathematical Reviews number (MathSciNet)
MR2829890

Zentralblatt MATH identifier
1239.49007

Subjects
Primary: 49J30: Optimal solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) 49J40: Variational methods including variational inequalities [See also 47J20] 47J25: Iterative procedures [See also 65J15] 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.

Keywords
strictly pseudocontractive mapping fixed point inverse-strongly-monotone mapping variational inequality generalized mixed equilibrium problem with perturbed mapping system of generalized nonlinear mixed composite-type equilibria

Citation

Hu, Hui-Ying; Ceng, Lu-Chuan. A General System of Generalized Nonlinear Mixed Composite-Type Equilibria in Hilbert Spaces. Taiwanese J. Math. 15 (2011), no. 3, 927--959. doi:10.11650/twjm/1500406276. https://projecteuclid.org/euclid.twjm/1500406276


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