A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings

We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi...

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Main Authors: Pongrus Phuangphoo, Poom Kumam
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/107296
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spelling doaj-44ed055bc4584afa8ac95b6b9f2bd0512020-11-24T22:01:48ZengHindawi LimitedAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/107296107296A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive MappingsPongrus Phuangphoo0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Kru, Bangkok 10140, ThailandWe introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.http://dx.doi.org/10.1155/2013/107296
collection DOAJ
language English
format Article
sources DOAJ
author Pongrus Phuangphoo
Poom Kumam
spellingShingle Pongrus Phuangphoo
Poom Kumam
A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
Abstract and Applied Analysis
author_facet Pongrus Phuangphoo
Poom Kumam
author_sort Pongrus Phuangphoo
title A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
title_short A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
title_full A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
title_fullStr A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
title_full_unstemmed A New Hybrid Projection Algorithm for System of Equilibrium Problems and Variational Inequality Problems and Two Finite Families of Quasi-ϕ-Nonexpansive Mappings
title_sort new hybrid projection algorithm for system of equilibrium problems and variational inequality problems and two finite families of quasi-ϕ-nonexpansive mappings
publisher Hindawi Limited
series Abstract and Applied Analysis
issn 1085-3375
1687-0409
publishDate 2013-01-01
description We introduce a modified Mann’s iterative procedure by using the hybrid projection method for solving the common solution of the system of equilibrium problems for a finite family of bifunctions satisfying certain condition, the common solution of fixed point problems for two finite families of quasi-ϕ-nonexpansive mappings, and the common solution of variational inequality problems for a finite family of continuous monotone mappings in a uniformly smooth and strictly convex real Banach space. Then, we prove a strong convergence theorem of the iterative procedure generated by some mild conditions. Our result presented in this paper improves and generalizes some well-known results in the literature.
url http://dx.doi.org/10.1155/2013/107296
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