ordered $b$-metric space

In this paper, recalling the structure of modified G-metric spaces (as a generalization of both G-metric and Gb-metric spaces), we present the notions of G-rational contractive mappings and investigate the existence of fixed point for such mappings. We also provide examples and an application to illustrate the results presented herein.

In this paper, we introduce the notion of an extended metric space ($p$-metric space) as a new generalization of the concept of $b$-metric space. Also, we present the concept of $(psi ,varphi )_{Omega}$-contractive mappings and we establish some fixed point results for this class of mappings in ordered complete $p$-metric spaces. Our results generalize several well-known comparable results in the literature. Finally, examples support our results.

In this paper, we present some fixed and coincidence point theorems for hybrid rational Geraghty contractive mappings in partially ordered b-metric spaces. Also, we derive certain coincidence point results for such contractions. An illustrative example is provided here to highlight our findings.

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fixed pointtheorem in ordered generalized $b$-metric spaces is equivalentwith Ran-Reurings-type theorem in ordered $b$-metric spaces.