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In this paper, by characterizing a weak contractive condition based on using C − functions and α − admissible multi-valued mapping of type S, we present some fixed point results for ( α , F ) − admissible multi-valued mappings in the setting of b − metric spaces. Some examples and an application are added in order to show the reliability of our obtained results. Our results amend, unify, and generalize some existing results in the literature. The scientific novelty of our main results is todoi:10.3390/math7020132 fatcat:sbhuvjrcbrauxianfyroqvyoaq