Author(s)

Yi Li

School of Science, Southwest University of Science and Technology, Mianyang, China.

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).

Multi-Valued Mapping; Totally Quasi- Ø -Asymptotically Nonexpansive; Countable Family of Uniformly Totally Quasi- Ø -Asymptotically Nonexpansive Multi-Valued Mappings; Firmly Convergence

Y. Li, "Fixed Point of a Countable Family of Uniformly Totally Quasi- 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.