A new modified block iterative algorithm for uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems
<p>Abstract</p> <p>In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings, the set o...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2011-01-01
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| Series: | Fixed Point Theory and Applications |
| Subjects: | |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2011/1/35 |
| Summary: | <p>Abstract</p> <p>In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-<it>ϕ</it>-asymptotically nonexpansive mappings, the set of the variational inequality for an <it>α</it>-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works.</p> <p> <b>2000 MSC: </b>47H05; 47H09; 47H10.</p> |
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| ISSN: | 1687-1820 1687-1812 |