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2013 Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces
Lu-Chuan Ceng, Abdul Latif, Abdullah E. Al-Mazrooei
Abstr. Appl. Anal. 2013(SI09): 1-18 (2013). DOI: 10.1155/2013/328740

Abstract

We introduce Mann-type viscosity approximation methods for finding solutions of a multivalued variational inclusion (MVVI) which are also common ones of finitely many variational inequality problems and common fixed points of a countable family of nonexpansive mappings in real smooth Banach spaces. Here the Mann-type viscosity approximation methods are based on the Mann iteration method and viscosity approximation method. We consider and analyze Mann-type viscosity iterative 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 Gáteaux differentiable norm. Under suitable assumptions, we derive some strong convergence theorems. In addition, we also give some applications of these theorems; for instance, we prove strong convergence theorems for finding a common fixed point of a finite family of strictly pseudocontractive mappings and a countable family of nonexpansive mappings in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

Citation

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Lu-Chuan Ceng. Abdul Latif. Abdullah E. Al-Mazrooei. "Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces." Abstr. Appl. Anal. 2013 (SI09) 1 - 18, 2013. https://doi.org/10.1155/2013/328740

Information

Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1364.47012
MathSciNet: MR3139443
Digital Object Identifier: 10.1155/2013/328740

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI09 • 2013
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