Strong convergence theorem for amenable semigroups of nonexpansive mappings and variational inequalities
<p>Abstract</p> <p>In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate...
| 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/2011/1/55 |
| Summary: | <p>Abstract</p> <p>In this paper, using strongly monotone and lipschitzian operator, we introduce a general iterative process for finding a common fixed point of a semigroup of nonexpansive mappings, with respect to strongly left regular sequence of means defined on an appropriate space of bounded real-valued functions of the semigroups and the set of solutions of variational inequality for <it>β</it>-inverse strongly monotone mapping in a real Hilbert space. Under suitable conditions, we prove the strong convergence theorem for approximating a common element of the above two sets.</p> <p> <b>Mathematics Subject Classification 2000: </b>47H09, 47H10, 43A07, 47J25</p> |
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| ISSN: | 1687-1820 1687-1812 |