Abstract
In this article, we obtain fixed point results under some rational contractive conditions for mappings in the setup of ordered ρ-metric spaces. Also, three examples and an application to existence ...
Highlights
The field of extension of metric space is a growing field these years
We introduce some type of Geraghty contractive mappings and comparison contractive mappings in extended b-metric spaces and we establish some fixed point results in complete partially ordered extended b-metric spaces
Metric fixed point theory is a powerful tool for solving several problems in various parts of mathematics and its applications
Summary
The field of extension of metric space is a growing field these years. The famous extensions of the concept of metric spaces have been done by (Czerwik, 1993) and (Matthews, 1994) where they introduced and studied the concepts of b-metric spaces and partial metric spaces, respectively. We introduce some type of Geraghty contractive mappings and comparison contractive mappings in extended b-metric spaces and we establish some fixed point results in complete partially ordered extended b-metric spaces. 1. For more details on fixed point results and their applications in b-metric spaces we refer the reader to (Ali, Kamran, & Postolache, 2017; Kamran, Postolache, Ali, & Kiran, 2016; Shatanawi, Pitea, & Lazovic, 2014). Motivated by the concept of b-metric spaces, the following further generalization has been recently presented by Parvaneh and Ghoncheh
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