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A hybrid iterative scheme for mixed equilibrium problems and fixed point problems

✍ Scribed by Lu-Chuan Ceng; Jen-Chih Yao

Publisher: Elsevier Science
Year: 2008
Tongue: English
Weight: 211 KB
Volume: 214
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2007.02.022

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✦ Synopsis

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a mixed equilibrium problem (MEP) and the set of common fixed points of finitely many nonexpansive mappings in a real Hilbert space. First, by using the well-known KKM technique we derive the existence and uniqueness of solutions of the auxiliary problems for the MEP. Second, by virtue of this result we introduce a hybrid iterative scheme for finding a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings. Furthermore, we prove that the sequences generated by the hybrid iterative scheme converge strongly to a common element of the set of solutions of MEP and the set of common fixed points of finitely many nonexpansive mappings.

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