A block hybrid method for solving generalized equilibrium problems and convex feasibility problem

Shih Sen Chang; Heung Wing Joseph Lee; Chi Kin Chan

doi:10.1007/s10444-011-9249-5

A block hybrid method for solving generalized equilibrium problems and convex feasibility problem

Shih Sen Chang, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

A block hybrid projection algorithm for solving the convex feasibility problem and the generalized equilibrium problems for an infinite family of total quasi-φ{symbol}-asymptotically nonexpansive mappings is introduced. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

Original language	English
Pages (from-to)	563-580
Number of pages	18
Journal	Advances in Computational Mathematics
Volume	38
Issue number	3
DOIs	https://doi.org/10.1007/s10444-011-9249-5
Publication status	Published - 1 Jan 2013

Keywords

Block iterative algorithm
Convex feasibility problem
Generalized equilibrium problem
Generalized projection
Quasi-φ{symbol}-nonexpansive mapping
Relatively nonexpansive mapping
Total quasi-φ{symbol}-asymptotically nonexpansive mapping

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1007/s10444-011-9249-5

Cite this

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title = "A block hybrid method for solving generalized equilibrium problems and convex feasibility problem",

abstract = "A block hybrid projection algorithm for solving the convex feasibility problem and the generalized equilibrium problems for an infinite family of total quasi-φ{symbol}-asymptotically nonexpansive mappings is introduced. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.",

keywords = "Block iterative algorithm, Convex feasibility problem, Generalized equilibrium problem, Generalized projection, Quasi-φ{symbol}-nonexpansive mapping, Relatively nonexpansive mapping, Total quasi-φ{symbol}-asymptotically nonexpansive mapping",

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AU - Lee, Heung Wing Joseph

AU - Chan, Chi Kin

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N2 - A block hybrid projection algorithm for solving the convex feasibility problem and the generalized equilibrium problems for an infinite family of total quasi-φ{symbol}-asymptotically nonexpansive mappings is introduced. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

AB - A block hybrid projection algorithm for solving the convex feasibility problem and the generalized equilibrium problems for an infinite family of total quasi-φ{symbol}-asymptotically nonexpansive mappings is introduced. Under suitable conditions some strong convergence theorems are established in uniformly smooth and strictly convex Banach spaces with Kadec-Klee property. The results presented in the paper improve and extend some recent results.

KW - Block iterative algorithm

KW - Convex feasibility problem

KW - Generalized equilibrium problem

KW - Generalized projection

KW - Quasi-φ{symbol}-nonexpansive mapping

KW - Relatively nonexpansive mapping

KW - Total quasi-φ{symbol}-asymptotically nonexpansive mapping

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U2 - 10.1007/s10444-011-9249-5

DO - 10.1007/s10444-011-9249-5

M3 - Journal article

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EP - 580

JO - Advances in Computational Mathematics

JF - Advances in Computational Mathematics

SN - 1019-7168

IS - 3

ER -

A block hybrid method for solving generalized equilibrium problems and convex feasibility problem

Abstract

Keywords

ASJC Scopus subject areas

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