Orthogonal F-Quasi-Contractions on O-Complete Metric Spaces with Applications

Abstract

In this paper, we introduce the notion of orthogonal F-quasi-contractions on orthogonal metric spaces. We establish two fixed point theorems for such mappings: one requiring orthogonal continuity and another in which this assumption is relaxed. When the orthogonality relation is taken to be universal, the results yield new fixed point theorems for F-quasi-contractions on complete metric spaces. We construct examples to show that the newly introduced notion overlaps with and extends the F-weak contractions and F-contractions notions to handle more complex, non-continuous, or asymmetrical mapping behaviors.

As an application, we prove the existence and uniqueness of a solution to an initial value problem for a general Volterra-type integro-differential equation. Such equations arise in various fields, including epidemic modeling, control theory, and physics.