Convergence Theorems Concerning Hybrid Methods for Strict Pseudocontractions and Systems of Equilibrium Problems
<p/> <p>Let <inline-formula> <graphic file="1029-242X-2010-396080-i1.gif"/></inline-formula> be <inline-formula> <graphic file="1029-242X-2010-396080-i2.gif"/></inline-formula> strict pseudo-contractions defined on a closed and conv...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2010/396080 |
| Summary: | <p/> <p>Let <inline-formula> <graphic file="1029-242X-2010-396080-i1.gif"/></inline-formula> be <inline-formula> <graphic file="1029-242X-2010-396080-i2.gif"/></inline-formula> strict pseudo-contractions defined on a closed and convex subset <inline-formula> <graphic file="1029-242X-2010-396080-i3.gif"/></inline-formula> of a real Hilbert space <inline-formula> <graphic file="1029-242X-2010-396080-i4.gif"/></inline-formula>. We consider the problem of finding a common element of fixed point set of these mappings and the solution set of a system of equilibrium problems by parallel and cyclic algorithms. In this paper, new iterative schemes are proposed for solving this problem. Furthermore, we prove that these schemes converge strongly by hybrid methods. The results presented in this paper improve and extend some well-known results in the literature.</p> |
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| ISSN: | 1025-5834 1029-242X |