In this paper, we study the uniqueness and existence of a common fixed point for a pair of mappings in cone metric space. The results extend and improve recent related results.
Fixed point theorems for mappings with convex diminishing diameters on cone metric spaces
✍ Scribed by Shahrazad H. Alnafei; Stojan Radenović; Naseer Shahzad
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 218 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0893-9659
No coin nor oath required. For personal study only.
✦ Synopsis
In this work, Cantor's intersection theorem is extended to cone metric spaces and as an application, a fixed point theorem is derived for mappings with locally power diminishing diameters.
📜 SIMILAR VOLUMES
In the present work, some fixed point and common fixed point theorems for self-maps on ordered cone metric spaces, where the cone is not necessarily normal, are proved.
point theorem of Imdad and Kumar, for a pair of non-self maps, to non-normal cone spaces.
In this paper, new contraction type non-self mappings in a metric space are introduced, and conditions guaranteeing the existence of a common fixed-point for such non-self contractions in a convex metric space are established. These results generalize and improve the recent results of Imdad and Khan
The notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham ( 2006) in [13]. In this manuscript, some results of Lakshmikantham and Ćirić (2009) in [5] are extended to the class of cone metric spaces.