$η$-metric structures

Abstract

In this paper, we discuss recent results about generalized metric spaces and fixed point theory. We introduce the notion of η-cone metric spaces, give some topological properties and prove some fixed point theorems for contractive type maps on these spaces. In particular we show that theses η-cone metric spaces are natural generalizations of both cone metric spaces and metric type spaces.

Fixed points on partial metric type spaces

“…From the above results, it is very clear that K-PMS represent quite a large class of "metric like" structures and such setting can be made even larger if we look at the work by Choi [2] and Gaba [5]. Using the same idea as in the proofs of Theorem 4.3 and Theorem 4.6, one can establish the following results.…”