Common Fixed Points for a Countable Family of Set-Valued Mappings with Quasi-Contractive Conditions on Metrically Convex Spaces

Yuexi Jin, Ailian Jin, Yongjie Piao

Department of Mathematics, College of Science, Yanbian University, Yanji, China.

DOI: 10.4236/apm.2014.41003                

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.

Keywords

Common Fixed Point; Quasi-Contractive; Metrically Convex; Complete

Conflicts of Interest

The authors declare no conflicts of interest.

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