Incomplete Metric With The Application For Integral Equations of Volterra Type

Abstract

In this article, we propose some weaker orthogonal $\left(\tau ,F_{\mathfrak{T}}\right)-$ type of contraction mappings in the setting of metric spaces endowed with an orthogonal relation, as well as certain sufficient criteria for the existence of fixed points for this class of mappings. To establish all of our results in the manuscript, we just used Wardowski’s strictly increasing property. Using the aforementioned results as an application, we demonstrate that the Volterra type integral equation has a solution and is stable in the Hyers-Ulam-Rassias-Wright sense.