BALANCED MAPPINGS AND AN ITERATIVE SCHEME IN COMPLETE GEODESIC SPACES

TAKUTO  KAJIMURA; KENGO  KASAHARA; YASUNORI  KIMURA; KOICHI  NAKAGAWA

BALANCED MAPPINGS AND AN ITERATIVE SCHEME IN COMPLETE GEODESIC SPACES

Authors

TAKUTO KAJIMURA Miyamoto Junior High School, Higashifunabashi, Funabashi, Chiba 273-0002, Japan
KENGO KASAHARA Department of Information Science, Toho University, Miyama, Funa-bashi, Chiba 274-8510, Japan
YASUNORI KIMURA Department of Information Science, Toho University, Miyama, Funa-bashi, Chiba 274-8510, Japan
KOICHI NAKAGAWA Department of Information Science, Toho University, Miyama, Funa-bashi, Chiba 274-8510, Japan

Keywords:

balanced mapping, iterative scheme, CAT(1) space, common fixed point

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.