Document Type : Research Paper

Author

• Sahar Mohamed Ali Abou Bakr

Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt

Abstract

This paper gives a study of various types of cone metric spaces and their topological characterizations. Contrarily to the case of cone metric space $X$, the paper shows with examples that the limit of a sequence may not be unique in the topology generated by partial cone metric $T_{p}$ and $(X, T_{p})$ is not generally Hausdorff topological space and also the cone valued partial metric mapping $p$ may not generally be continuous. Hence $T_{p}$ is not equivalent to any topology generated by any metric on $X$. Furthermore, the paper considers some generalized contraction types of mappings on $\theta$-complete cone metric-like spaces and then generalizes some coupled fixed point theorems of some previous results in this setting.

Keywords

• Partial Metric Spaces
• Cone Metric Like Spaces
• Cone Metric Spaces
• Partial Cone Metric Space
• coupled Fixed Point Theorems