Fixed Point Theorems in Orthogonal F-Metric Spaces

F-metric spaces are defined as a generalization of metric spaces with properties of nonnegativity, self-distance, symmetry and generalized triangular inequality. Moreover, notion of orthogonal F-metric spaces are introduced given by establishing a binary relation on the set. In this work, we give some properties of orthogonal relation on a set and some topological properties of orthogonal F-metric spaces. We introduce some rational type contractions in orthogonal F-metric spaces and prove fixed point theorems for this type contraction. Our results generalize the Jaggi and Ciric type contractions.