Some Fixed-Point Theorems in Proximity Spaces with Applications

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.

An Existence Result for Second-Order Boundary-Value Problems via New Fixed-Point Theorems on Quasi-Metric Space

“…where H : [0, 1] × R → R is a continuous function. In the literature, there have been existence theorems provided for the problem (10) that consider certain requirements on H (see [25][26][27][28][29][30]). In this instance, we will examine different conditions on H and offer a novel theorem.…”