Strong convergence theorems by hybrid block generalized f-projection method for fixed point problems of asymptotically quasi-φ-nonexpansive mappings and system of generalized mixed equilibrium problems
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Author list: Saewan S., Kumam P., Kim J.K.
Publication year: 2014
Journal: Thai Journal of Mathematics (1686-0209)
Volume number: 12
Issue number: 2
Start page: 275
End page: 301
Number of pages: 27
ISSN: 1686-0209
Languages: English-Great Britain (EN-GB)
Abstract
The purpose of this paper is to present a new hybrid block iterative scheme by the generalized f-projection method for finding a common element of the fixed point set for a countable family of uniformly asymptotically quasi-φ- nonexpansive mappings and the set of solutions of the system of generalized mixed equilibrium problems in a strictly convex and uniformly smooth Banach space with the Kadec-Klee property. Furthermore, we prove that our new hybrid block iterative scheme converges strongly to a common element of the afore mentioned sets. The results presented in this paper improve and extend important recent results in the literature. © 2014 by the Mathematical Association of Thailand. All rights reserved.
Keywords
Quasi-f-asymptotically nonexpansive mappings, System of generalized mixed equilibrium problem, The generalized f-projection operator
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