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Fixed Point of a Countable Family of Uniformly Totally Quasi- <i>Ø</i> -Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications
School of Science, Southwest University of Science and Technology, Mianyang, China
- 1 School of Science, Southwest University of Science and Technology, Mianyang, China
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Abstract
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).
KeywordsMulti-Valued MappingTotally Quasi- <i>&Oslash</i>-Asymptotically NonexpansiveCountable Family of Uniformly Totally Quasi-<i>&Oslash</i>-Asymptotically Nonexpansive Multi-Valued MappingsFirmly Convergence
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