Double controlled metric-like spaces

• Published in: Journal of inequalities and applications Vol. 2020; no. 1; pp. 1 - 12
• Main Author: Mlaiki, Nabil
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 17.07.2020; Springer Nature B.V; SpringerOpen
• Subjects: Analysis; Applications of Mathematics; b-Metric spaces; Controlled metric type spaces; Double controlled metric like spaces; Double controlled metric type spaces; Extended b-metric space; Fixed point; Fixed points (mathematics); Mathematics; Mathematics and Statistics; Metric space; metric space; Double controlled metric type spaces; 47H10; Controlled metric type spaces; Extended; Metric spaces; Double controlled metric like spaces; Fixed point; 54H25
• ISSN: 1029-242X; 1025-5834; 1029-242X
• DOI: 10.1186/s13660-020-02456-z

In this paper, we introduce a new extension of the double controlled metric-type spaces, called double controlled metric-like spaces, by assuming that the “self-distance” may not be zero On the other hand, if the value of the metric is zero, then it has to be a “self-distance” (i.e., we replace [ ς ( g , h ) = 0 ⇔ g = h ] by [ ς ( g , h ) = 0 ⇒ g = h ] ). Using this new type of metric spaces, we generalize many results in the literature. We prove fixed point results along with examples illustrating our theorems. Also, we present double controlled metric-like spaces endowed with a graph along with an open question.