A new general system of generalized nonlinear mixed composite-type equilibria and fixed point problems with an application to minimization problems
type: Item
instance of: scholarly article
title: A new general system of generalized nonlinear mixed composite-type equilibria and fixed point problems with an application to minimization problems
zbMATH Open document ID: 1296.47092
DOI: 10.1155/2012/414718
author: Pongsakorn Sunthrayuth
author: Poom Kumam
published in: Abstract and Applied Analysis
publication date: 2013-02-04T00:00:00Z
review text: Summary: We introduce a new general system of generalized nonlinear mixed composite-type equilibria and propose a new iterative scheme for finding a common element of the set of solutions of a generalized equilibrium problem, the set of solutions of a general system of generalized nonlinear mixed composite-type equilibria, and the set of fixed points of a countable family of strict pseudocontraction mappings. Furthermore, we prove the strong convergence theorem of the proposed iterative scheme in a real Hilbert space. As applications, we apply our results to solve a certain minimization problem related to a strongly positive bounded linear operator. Finally, we also give a numerical example which supports our results.
Mathematics Subject Classification ID: 47J25
Mathematics Subject Classification ID: 47H09
Mathematics Subject Classification ID: 47N10
Mathematics Subject Classification ID: 47B65
zbMATH DE Number: 6134085
zbMATH Keywords: nonlinear mixed composite-type equilibria
zbMATH Keywords: generalized equilibrium problem
zbMATH Keywords: fixed point
zbMATH Keywords: strict pseudocontraction mapping
zbMATH Keywords: strong convergence
zbMATH Keywords: real Hilbert space
zbMATH Keywords: minimization problem
zbMATH Keywords: strongly positive bounded linear operator
MaRDI profile type: Publication
Wikidata QID: Q58696576
full work available at URL: https://doi.org/10.1155/2012/414718
OpenAlex ID: W2132839273
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description: scientific article; zbMATH DE number 6134085