On some fixed point results in bb-metric, rectangular and bb-rectangular metric spaces

In this paper we consider, discuss, improve and generalize recent fixed point results for mappings in b  -metric, rectangular metric and bb-rectangular metric spaces established by Đukić et al. (2011), George and Rajagopalan (2013) and Roshan et al. (2015). Also, we prove a Geraghty type theorem in the setting of bb-metric spaces as well as a Boyd–Wong type theorem in the framework of bb-rectangular metric spaces, in both cases, without using Hausdorff assumption. One example is given to support the results.