Abstract
In this paper, two renowned fixed point results which belong to Presic and Heilpern in the context of metric and fuzzy fixed point theory are revisited. To this end, we initiate the study of Heilpern–Presic type fuzzy fixed point results through some generalized weakly contractive conditions in the framework of [Formula: see text]-metric spaces. A few counterparts of our results in the setting of multi-valued and single-valued mappings are noted and discussed. A nontrivial example is provided to validate the assertions of our theorems. Moreover, stability conditions of Presic type fuzzy set-valued maps are introduced and global attractivity result for a class of nonlinear matrix difference equations is also obtained as one of the applications of our results. The presented ideas herein complement and extend several significant results in the comparable literature.
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