Strong Convergence Theorems for Countable Families of Uniformly Quasi-ϕ-Asymptotically Nonexpansive Mappings and a System of Generalized Mixed Equilibrium Problems
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 quasi-ϕ-asymptotically nonexpansive mappings and the set of solutions of the system of generaliz...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/701675 |
| Summary: | 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
quasi-ϕ-asymptotically 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 iterative scheme converges strongly to a common element
of the aforementioned sets. The results presented in this paper improve and extend important recent
results in the literature. |
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| ISSN: | 1085-3375 1687-0409 |