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

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 Tp and (X, Tp) is not generally Hausdorff topological space and also the cone valued partial metric mapping p may not generally be continuous. Hence Tp is not equivalent to any topology generated by any metric on X. Furthermore, the paper considers some generalized contraction types of mappings on θ-complete cone metric-like spaces and then generalizes some coupled fixed point theorems of some previous results in this setting.