Abstract
In this study, we introduce the concept of θ-expansive mapping in ordered metric spaces and prove a fixed point theorem for such mappings. We give some fixed point results for θ-expansive mapping in metric spaces and prove fixed point theorems for such mappings. These results extend the main results of many comparable results from the current literature. We also obtain a common fixed point theorem of two weakly compatible mappings in metric spaces. Finally, the examples are presented to support the new theorems and results proved.
Highlights
The study of expansive mappings is a very interesting research area in the fixed point theory.Wang et al [1] proved some fixed point theorems for expansion mappings, which correspond to some contractive mappings in metric spaces
We introduce a fixed point theorem for θ-expansive mapping on ordered metric spaces
Wang et al [1], proved some fixed point theorems for expansive mappings, which correspond to some contractive mappings in metric spaces
Summary
The study of expansive mappings is a very interesting research area in the fixed point theory.Wang et al [1] proved some fixed point theorems for expansion mappings, which correspond to some contractive mappings in metric spaces. Thereafter, several authors obtained many fixed point theorems for expansive mappings. Ran and Reurings [11] proved a fixed point theorem on a partially ordered metric space as follow: Mathematics 2020, 8, 1800; doi:10.3390/math8101800 We introduce a fixed point theorem for θ-expansive mapping on ordered metric spaces.
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