Hybrid proximal-point methods for zeros of maximal monotone operators, variational inequalities and mixed equilibrium problems

Journal article

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POOM KUMAM

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Publication Details

Author list: Kumam P., Wattanawitoon K.

Publisher: Hindawi

Publication year: 2011

Journal: International Journal of Mathematics and Mathematical Sciences (0161-1712)

Volume number: 2011

ISSN: 0161-1712

eISSN: 1687-0425

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-79953272859&doi=10.1155%2f2011%2f174796&partnerID=40&md5=0dec2d5e8ba7970607d5744a11e7acc0

Languages: English-Great Britain (EN-GB)

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Abstract

We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors. Copyright 2011 Kriengsak Wattanawitoon and Poom Kumam.

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