A relaxed hybrid steepest descent method for common solutions of generalized mixed equilibrium problems and fixed point problems

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Publication Details

Author list: Onjai-uea N., Jaiboon C., Kumam P.

Publisher: SpringerOpen

Publication year: 2011

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2011

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902520011&doi=10.1186%2f1687-1812-2011-32&partnerID=40&md5=a29cf81d2bbf315e1e59515c24264c44

Languages: English-Great Britain (EN-GB)

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Abstract

In the setting of Hilbert spaces, we introduce a relaxed hybrid steepest descent method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of a variational inequality for an inverse strongly monotone mapping and the set of solutions of generalized mixed equilibrium problems. We prove the strong convergence of the method to the unique solution of a suitable variational inequality. The results obtained in this article improve and extend the corresponding results. ฉ 2011 Onjai-uea et al; licensee Springer.

Keywords

Inverse strongly monotone mappings, Relaxed hybrid steepest descent method