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Common Fixed Points for a Countable Family of Set-Valued Mappings with Quasi-Contractive Conditions on Metrically Convex Spaces
Department of Mathematics, College of Science, Yanbian University, Yanji, China
Department of Mathematics, College of Science, Yanbian University, Yanji, China
Department of Mathematics, College of Science, Yanbian University, Yanji, China
- 1 Department of Mathematics, College of Science, Yanbian University, Yanji, China
- 2 Department of Mathematics, College of Science, Yanbian University, Yanji, China
- 3 Department of Mathematics, College of Science, Yanbian University, Yanji, China
Advances in Pure Mathematics·Volume 04 (2014)·Pages 17–24·Published 8 January 2014·DOI10.4236/apm.2014.41003
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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.
KeywordsCommon Fixed PointQuasi-ContractiveMetrically ConvexComplete
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