## Journal of Applied Mathematics

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

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

**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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