Journal of Applied Mathematics

Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings

Poom Kumam, Usa Hamphries, and Phayap Katchang

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Abstract

We introduce a new iterative scheme by shrinking projection method for finding a common element of the set of solutions of generalized mixed equilibrium problems, the set of common solutions of variational inclusion problems with set-valued maximal monotone mappings and inverse-strongly monotone mappings, the set of solutions of fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above four sets under some mind conditions. Furthermore, by using the above result, an iterative algorithm for solution of an optimization problem was obtained. Our results improve and extend the corresponding results of Martinez-Yanes and Xu (2006), Shehu (2011), Zhang et al. (2008), and many authors.

Article information

Source
J. Appl. Math., Volume 2011 (2011), Article ID 953903, 28 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331818630

Digital Object Identifier
doi:10.1155/2011/953903

Mathematical Reviews number (MathSciNet)
MR2830754

Zentralblatt MATH identifier
1297.47084

Citation

Kumam, Poom; Hamphries, Usa; Katchang, Phayap. Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings. J. Appl. Math. 2011 (2011), Article ID 953903, 28 pages. doi:10.1155/2011/953903. https://projecteuclid.org/euclid.jam/1331818630


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