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In this paper we consider, discuss, improve and generalize recent fixed point results for mappings in b-metric, rectangular metric and b-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 b-metric spaces as well as a Boyd–Wong type theorem in the framework of b-rectangular metric spaces, in both cases, without using Hausdorff assumption. One example is given to support the results.