Rational Geraghty Contractive Mappings and Fixed Point Theorems in Ordered b2-metric Spaces

In 2014, Zead Mustafa introduced b2-metric spaces, as a generalization of both 2-metric and b-metric spaces. Then new xed point results for the classes of rational Geraghty contractive mappings of type I,II and III in the setup of b2-metric spaces are investigated. Then, we prove some fixed point theorems under various contractive conditions in partially ordered b2-metric spaces. These include Geraghty-type conditions, conditions that use com- parison functions and almost generalized weakly contractive conditions. Berinde in [17-20] initiated the concept of almost contractions and obtained many interesting fixed point theorems. Results with similar conditions were obtained, e.g., in [21] and [22]. In the last section of the paper, we de ne the notion of almost general- ized (ψ ; φ)s;a-contractive mappings and prove some new results. In particular, we extend Theorems 2.1, 2.2 and 2.3 of Ciri c et.al. in [23] to the setting of b2-metric spaces. Also, some examples are provided to illustrate the results presented herein and several inter- esting consequences of our theorems are also provided. The ndings of the paper are based on generalization and modi cation of some recently reported theorems in the literature.