Open AccessFixed Point of a Countable Family of Uniformly Totally Quasi- <i>&Oslash</i> -Asymptotically Nonexpansive Multi-Valued Mappings in Reflexive Banach Spaces with Applications
Author(s) -
Yi Li
Publication year - 2013
Publication title -
applied mathematics
Language(s) - English
Resource type - Journals
eISSN - 2152-7393
pISSN - 2152-7385
DOI - 10.4236/am.2013.49a002
Subject(s) - countable set , mathematics , fixed point , banach space , convergence (economics) , type (biology) , fixed point theorem , discrete mathematics , computation , pure mathematics , mathematical analysis , algorithm , ecology , economics , economic growth , biology
The purpose of this article is to discuss a modified Halpern-type iteration algorithm for a countable family of uniformly totally quasi- Ø -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).