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Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

Karapınar Erdal, Romaguera Salvador, Tirado Pedro

Demonstratio Mathematica

2022

Vol. 55, nr 1

939--951

Involving w-distances we prove a fixed point theorem of Caristi-type in the realm of (non-necessarily T1) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. Our approach allows us to retrieve several key examples occurring in various fields of mathematics and computer science and that are modeled as non- T1 quasi-metric spaces. As an application, we deduce a characterization of complete G -metric spaces in terms of a weak version of Caristi’s theorem that involves a G-metric version of w-distances.

Fixed point results in complete metric spaces

Latif A., Albar W.

Demonstratio Mathematica

2008

Vol. 41, nr 1

145-150

Using the concept of w-distance, we prove fixed point theorems for multivalued contractive maps. Consequently, we improve and extend the corresponding fixed point results due to Feng and Liu, Nadler and many of others.