Qasim, MuhammadAlamri, HindAltun, IshakHussain, Nawab2025-01-212025-01-2120222227-7390https://doi.org/10.3390/math10101724https://hdl.handle.net/20.500.12587/25464Considering the omega-distance function defined by Kostic in proximity space, we prove the Matkowski and Boyd-Wong fixed-point theorems in proximity space using omega-distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.eninfo:eu-repo/semantics/openAccessfixed point; proximity spaces; phi-contraction; omega-distanceArticle101010.3390/math101017242-s2.0-85130942860Q1WOS:000801661500001Q1