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, issue 1

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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https://doi.org/10.1155/2013/328740

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:328740

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