Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings
We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone map...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2011-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2011/953903 |
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| Summary: | We introduce a new iterative scheme by shrinking projection method for finding a common
element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of
variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone
mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed
points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that
the sequence converges strongly to a common element of the above four sets under some mind conditions.
Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was
obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu
(2011), Zhang et al. (2008), and many authors. |
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| ISSN: | 1110-757X 1687-0042 |