BALANCED MAPPINGS AND AN ITERATIVE SCHEME IN COMPLETE GEODESIC SPACES

T. Kajimura; K. Kasahara; Y.  Kimura; K. Nakagawa

BALANCED MAPPINGS AND AN ITERATIVE SCHEME IN COMPLETE GEODESIC SPACES

Authors

T. Kajimura Miyamoto Junior High School, Higashifunabashi, Funabashi, Chiba 273-0002, Japan
K. Kasahara Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan
Y. Kimura Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan
K. Nakagawa Department of Information Science, Toho University, Miyama, Funabashi, Chiba 274-8510, Japan

Keywords:

common fixed point, CAT(1) space, quasinonexpansive, Mann type, iteration

Abstract

In this paper, we define a balanced mapping by a maximizer of a certain function generated by a finite number of mappings without regard to their order and find its fundamental properties in a complete CAT(1) space. Furthermore, we approximate a fixed point of a balanced mapping which is generated by a finite number of quasinonexpansive and $\Delta$ -demiclosed mappings by using Mann's iterative scheme.