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Fixed Point of a Countable Family of Uniformly Totally Quasi- *Ø* -Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications

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The purpose of this article is to discuss a modified
Halpern-type iteration algorithm for a countable family of uniformly totally
quasi- *?* -asymptotically nonexpansive multi-valued mappings and
establish some strong convergence theorems under certain conditions. We utilize
the theorems to study a modified Halpern-type iterative algorithm for a system
of equilibrium problems. The results improve and extend the corresponding
results of Chang *et al*. (Applied
Mathematics and Computation, 218, 6489-6497).

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

*Ø*-Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications,"

*Applied Mathematics*, Vol. 4 No. 9A, 2013, pp. 6-12. doi: 10.4236/am.2013.49A002.

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