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In this study, we introduce a new notion, so-called <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>K</mi><mi>W</mi></mrow></semantics></math></inline-formula>-type <i>F</i>-contraction mapping, inspired by the ideas of Wardowski and Klim–Wardowski. Then, we investigate the existence of a best proximity point for such mappings by considering a new family, which is larger than the family of functions that is often used in fixed-point results for multivalued mappings. To demonstrate the effectiveness of our result, we also give a comparative example to which similar results in the literature cannot be applied. Moreover, we present an application of our main result to homotopic mappings.