The shrinking projection method for solving generalized equilibrium problems and common fixed points for asymptotically quasi-φ-nonexpansive mappings

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Publication Details

Author list: Saewan S., 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-s2.0-80054973548&doi=10.1186%2f1687-1812-2011-9&partnerID=40&md5=cabcd0c541b42916bfd1aea672524a3f

Languages: English-Great Britain (EN-GB)

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Abstract

In this article, we introduce a new hybrid projection iterative scheme based on the shrinking projection method for finding a common element of the set of solutions of the generalized mixed equilibrium problems and the set of common fixed points for a pair of asymptotically quasi-φ-nonexpansive mappings in Banach spaces and set of variational inequalities for an α-inverse strongly monotone mapping. The results obtained in this article improve and extend the recent ones announced by Matsushita and Takahashi (Fixed Point Theory Appl. 2004(1):37-47, 2004), Qin et al. (Appl. Math. Comput. 215:3874-3883, 2010), Chang et al. (Nonlinear Anal. 73:2260-2270, 2010), Kamraksa and Wangkeeree (J. Nonlinear Anal. Optim.: Theory Appl. 1 (1):55-69, 2010) and many others. AMS Subject Classification: 47H05, 47H09, 47J25, 65J15. © 2011 Saewan and Kumam; licensee Springer.

Keywords

Asymptotically quasi-φ- nonexpansive mapping, Banach spaces, Strong convergence theorem