A viscosity hybrid steepest descent method for generalized mixed equilibrium problems and variational inequalities for relaxed cocoercive mapping in hilbert spaces

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Jaiboon C., Chantarangsi W., Kumam P.

Publisher: Hindawi

Publication year: 2010

Journal: Abstract and Applied Analysis (1085-3375)

Volume number: 2010

ISSN: 1085-3375

eISSN: 1687-0409

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-77956719536&doi=10.1155%2f2010%2f390972&partnerID=40&md5=c5febbabbc60663f8fae0cf307f7a6a7

Languages: English-Great Britain (EN-GB)

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Abstract

We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems. Our method is based on the so-called viscosity hybrid steepest descent method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality. The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature. Copyright ฉ 2010 Wanpen Chantarangsi et al.

Keywords