In the present paper‎, ‎we‎ ‎define a new class of implicit contractions for a sequence of‎ ‎multi-valued mappings on a metric space endowed with a graph to‎ ‎obtain sufficient conditions for existence of common fixed points‎ ‎for this sequence‎. ‎This will enable us to obtain a simultaneous‎ ‎generalization of various types of fixed point theorems for a‎ ‎sequence of multi-valued mappings‎. ‎Moreover‎, ‎multi-fractal‎ ‎operators related to these contractive mappings are considered‎.

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