On various types of cone metric spaces and some applications in fixed point theory

Document Type : Research Paper


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


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.


Volume 14, Issue 1
January 2023
Pages 163-184
  • Receive Date: 21 July 2021
  • Revise Date: 21 August 2021
  • Accept Date: 01 September 2021