Mann-Type Viscosity Approximation Methods for Multivalued Variational Inclusions with Finitely Many Variational Inequality Constraints in Banach Spaces

Lu-Chuan Ceng, Abdul Latif and Abdullah E. Al-Mazrooei

Abstract and Applied Analysis, 2013, vol. 2013, 1-18

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:328740

DOI: 10.1155/2013/328740

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