Prešić-type fixed point results via Q-distance on quasimetric space and application to (p, q)-difference equations

Abstract

In this paper, we introduce two new properties to the Q-function, called as the 0-property and the small self-distance property, which is frequently used in studies of fixed point theory in quasimetric spaces. Then, with the help of Q-functions having these properties, we present some fixed point theorems for Prešić-type mappings in quasimetric spaces. Finally, we state a theorem for the existence and uniqueness of the solution to a boundary value problem for (p, q)-difference equations to demonstrate the applicability of our theoretical results, which we support with an example.