Abstract
Very recently, Miculescu and Mihail in (J. Fixed Point Theory Appl 19:2153–2163, 2017) gave a sufficient condition for Cauchyness on sequences in b-metric spaces. In this paper, we give a weaker sufficient condition. Also, to show the new sufficient condition is reasonably weak, we give an example. Using the new sufficient condition, we prove fixed point theorems for set-valued F-contractions in complete b-metric spaces. We also prove a fixed point theorem for single-valued F-contractions in complete b-metric spaces.
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