## Abstract and Applied Analysis

### Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings

#### Abstract

We introduce hybrid and relaxed Mann iteration methods for a general system of variational inequalities with solutions being also common solutions of a countable family of variational inequalities and common fixed points of a countable family of nonexpansive mappings in real smooth and uniformly convex Banach spaces. Here, the hybrid and relaxed Mann iteration methods are based on Korpelevich’s extragradient method, viscosity approximation method, and Mann iteration method. Under suitable assumptions, we derive some strong convergence theorems for hybrid and relaxed Mann iteration algorithms not only in the setting of uniformly convex and 2-uniformly smooth Banach space but also in a uniformly convex Banach space having a uniformly Gateaux differentiable norm. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

#### Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 102820, 44 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393449677

Digital Object Identifier
doi:10.1155/2013/102820

Mathematical Reviews number (MathSciNet)
MR3134168

Zentralblatt MATH identifier
1364.47011

#### Citation

Ceng, L. C.; Al-Mazrooei, A. E.; Abdou, A. A. N.; Latif, A. Hybrid and Relaxed Mann Iterations for General Systems of Variational Inequalities and Nonexpansive Mappings. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 102820, 44 pages. doi:10.1155/2013/102820. https://projecteuclid.org/euclid.aaa/1393449677

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