Modified Hybrid Block Iterative Algorithm for Convex Feasibility Problems and Generalized Equilibrium Problems for Uniformly Quasi-φ-Asymptotically Nonexpansive Mappings

We introduce a modified block hybrid projection algorithm for solving the convex feasibility problems for an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem f...

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Bibliographic Details
Published in:Abstract and Applied Analysis Vol. 2010; no. 2010; pp. 797 - 818
Main Authors: Saewan, Siwaporn, Kumam, Poom
Format: Journal Article
Language:English
Published: Hindawi Limiteds 01.01.2010
Hindawi Publishing Corporation
Wiley
Subjects:
Algorithms
Banach space
Blocking
Convergence
Feasibility
Iterative algorithms
Mapping
Projection
Theorems
ISSN:1085-3375, 1687-0409
Online Access:Get full text
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Summary:We introduce a modified block hybrid projection algorithm for solving the convex feasibility problems for an infinite family of closed and uniformly quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a uniformly smooth and strictly convex Banach space with Kadec-Klee property. The results presented in this paper improve and extend some recent results.
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ISSN:1085-3375
1687-0409
DOI:10.1155/2010/357120