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Let (M,δ) be a metric space, f:M→M, and g:M→[0,+∞). In this paper, we obtain sufficient conditions under which the set of fixed points of f is g-admissible, i.e., Fix(f)≠∅ and Fix(f)⊂g−10. Some special cases of our main results are discussed and some examples are given.

On the Admissibility of the Fixed Points Set of a Mapping with Respect to Another Mapping