Abstract
Considering the ω-distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using ω-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.