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Commun. Korean Math. Soc. 2016; 31(3): 507-518
Printed July 31, 2016
https://doi.org/10.4134/CKMS.c150173
Copyright © The Korean Mathematical Society.
Common fixed points for single-valued and multi-valued mappings in complete $\mathbb{R}$-trees
Withun Phuengrattana and Sirichai Sopha
Nakhon Pathom Rajabhat University, Nakhon Pathom Rajabhat University
The aim of this paper is to prove some strong convergence theorems for the modified Ishikawa iteration process involving a pair of a generalized asymptotically nonexpansive single-valued mapping and a quasi-nonexpansive multi-valued mapping in the framework of $\mathbb{R}$-trees under the gate condition.
Keywords: generalized asymptotically nonexpansive mapping, quasi-non\-expansive mapping, $\mathbb{R}$-trees, gate condition
MSC numbers: Primary 47H09, 47H10
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