In this paper we present fixed point theorem for nonlinear quasi-contractive mappings defined on TVS-cone metric space, which generalizes earlier results obtained by Ilić and Rakočević [D.
Quasi-contraction on a cone metric space
✍ Scribed by Dejan Ilić; Vladimir Rakočević
- Publisher
- Elsevier Science
- Year
- 2009
- Tongue
- English
- Weight
- 317 KB
- Volume
- 22
- Category
- Article
- ISSN
- 0893-9659
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✦ Synopsis
In this work we define and study quasi-contraction on a cone metric space. For such a mapping we prove a fixed point theorem. Among other things, we generalize a recent result of H. L. Guang and Z. Xian, and the main result of Ćirić is also recovered.
📜 SIMILAR VOLUMES
Using an old M. Krein's result and a result concerning symmetric spaces from [S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces, Banach J. Math. Anal. 5 (1) (2011), 38-50], we show in a very short way that all fixed point results in cone metric spaces obtained rec
Cone metric spaces are generalizations of metric spaces, where the metric is Banach spacevalued. Weak contractions are generalizations of the Banach's contraction mapping, which have been studied by several authors. In the present work, we establish a unique fixed point result for weak contractions
The concept of a 2-metric space hw been investigated by 5. G~ELER in a seriea of papers [6]-[S]. Other papers dealing with 2-metric spaces are [3]-[S], [lo], and [ 123. In this note several fixed point theorems a m proved for contractive mappings in a 2-metric space. The contradive definitions used