Some Extensions of Banach's Contraction Principle in Complete Cone Metric Spaces
By P. Raja, S. M. Vaezpour. 2008
103 citations recorded by the source corpus.
In this paper we consider complete cone metric spaces. We generalize some definitions such as -nonexpansive and -uniformly locally contractive functions -closure, -isometric in cone metric spaces, and certain fixed point theorems will be proved in those spaces. Among other results, we prove some interesting applications for the fixed point theorems in cone metric spaces.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/90ee6ef799a8bbba0b007172eb74f212b7580a26
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In Geometry and Topology
- Muhammad Arshad
- Akbar Azam
- Pasquale Vetro
- Cristina Di Bari
- Weicheng Mao
- Yuqiang Feng
- Zoran Kadelburg
- Stojan Radenovic
Citations in the corpus
- Weakly φ-pairs and common fixed points in cone metric spaces (2009, background): “The study of fixed and common fixed point theorems in cone metric spaces is followed by some other mathematicians, see [2–4,7,8,10].”
- COMMON FIXED POINTS OF GENERALIZED CONTRACTIVE MAPS IN CONE METRIC SPACES (2011, background): “Subsequently, some other authors [1, 2, 4-7] studied the existence of fixed points of self mappings satisfying a contractive type condition.”
- THE EQUIVALENCE OF CONE METRIC SPACES AND METRIC SPACES (2010, background): “Then in [10, 9, 7, 12, 8, 1], the authors extend some fixed point theorems on metric spaces to cone metric spaces.”