TITLE:
Common Fixed Points for a Countable Family of Set-Valued Mappings with Quasi-Contractive Conditions on Metrically Convex Spaces
AUTHORS:
Yuexi Jin, Ailian Jin, Yongjie Piao
KEYWORDS:
Common Fixed Point; Quasi-Contractive; Metrically Convex; Complete
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.1,
January
8,
2014
ABSTRACT: In this paper, we consider
a countable family of set-valued mappings satisfying some quasi-contractive
conditions. We also construct a sequence by the quasi-contractive conditions of
mappings and the boundary condition of a closed subset of a metrically convex
space, and then prove that the unique limit of the sequence is the unique
common fixed point of the mappings. Finally, we give more generalized common
fixed point theorems for a countable family of single-valued
mappings. The main results generalize and improve many common fixed point
theorems for a finite or countable family of single valued or set-valued mappings
with quasi-contractive conditions.