Journal of Applied Mathematics

A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators

Yaqin Wang

Full-text: Open access

Abstract

We introduce a new hybrid iterative scheme for finding a common element of the set of common fixed points of two countable families of relatively quasi-nonexpansive mappings, the set of the variational inequality, the set of solutions of the generalized mixed equilibrium problem, and zeros of maximal monotone operators in a Banach space. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results obtained in this paper improve and extend the result of Zeng et al. (2010) and many others.

Article information

Source
J. Appl. Math., Volume 2012 (2012), Article ID 712651, 21 pages.

Dates
First available in Project Euclid: 15 March 2012

Permanent link to this document
https://projecteuclid.org/euclid.jam/1331817622

Digital Object Identifier
doi:10.1155/2012/712651

Mathematical Reviews number (MathSciNet)
MR2854981

Zentralblatt MATH identifier
1235.65070

Citation

Wang, Yaqin. A New Hybrid Method for Equilibrium Problems, Variational Inequality Problems, Fixed Point Problems, and Zero of Maximal Monotone Operators. J. Appl. Math. 2012 (2012), Article ID 712651, 21 pages. doi:10.1155/2012/712651. https://projecteuclid.org/euclid.jam/1331817622


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