Geraghty–𝔽‐Contraction Type Darbo Fixed‐Point Theorems With an Application

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In this study, Darbo’s fixed‐point theorem is extended by employing Geraghty–𝔽‐contractions on Banach spaces. The obtained results are then applied to establish the existence of solutions for a fractional integral equation in the space C ([0, ς ]), equipped with the Hausdorff measure of noncompactness. To support and validate the main theorems presented, several illustrative examples are provided, highlighting the applicability and effectiveness of the theoretical findings. Moreover, for enhanced clarity and better comprehension, the examples are accompanied by figures and graphical representations, offering a visual demonstration of the practical relevance of the results.