A duality of generalized metric spaces

A Fixed Point Theorem in Generalized D-metric Spaces

Complete Generalized Metric Spaces

The well-known Banach’s fixed point theorem asserts that ifD X, f is contractive and X, d is complete, then f has a unique fixed point inX. It is well known that the Banach contraction principle 1 is a very useful and classical tool in nonlinear analysis. In 1969, Boyd and Wong 2 introduced the notion ofΦ-contraction. A mapping f : X → X on a metric space is called Φ-contraction if there exists...

On the topological equivalence of some generalized metric spaces

‎The aim of this paper is to establish the equivalence between the concepts‎ ‎of an $S$-metric space and a cone $S$-metric space using some topological‎ ‎approaches‎. ‎We introduce a new notion of a $TVS$-cone $S$-metric space using‎ ‎some facts about topological vector spaces‎. ‎We see that the known results on‎ ‎cone $S$-metric spaces (or $N$-cone metric spaces) can be directly obtained‎ from...

On Generalized Probabilistic Metric Spaces

In the present paper we study some generalized probabilistic metric spaces. Relationships with another deterministic and probabilistic metric structures are analyzed. A contraction condition for mappings with values into such a generalized probabilistic metric space is given. Fixed point results are proved.

On Generalized Complete Metric Spaces