A practical approach to fixed point theory in partial-metric spaces using simulation functions Fixed point theory in partial-metric spaces
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Abstract
This paper investigates coincidence point results for self-mappings in partial-metric spaces via simulation functions. By introducing a generalized contraction condition involving a simulation function and an auxiliary mapping $H$, we establish sufficient conditions for the existence and uniqueness of coincidence points and common fixed points. Our approach not only unifies several existing fixed point theorems in the literature but also provides a genuine extension by weakening conventional contraction assumptions. The theoretical findings are illustrated by a concrete example in a nonstandard partial-metric space setting, confirming the applicability and effectiveness of the proposed framework. As a special case, our results recover and generalize recent fixed point theorems in both metric and partial-metric spaces.
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