Fixed Point Results via Orthogonal (α - 𝔶 - 𝔾)-Contraction in Orthogonal Complete Metric Space.

In this publication, we establish a suitable symmetry structure for orthogonal (α−y−G)-contractive mappings and prove fixed point results for an orthogonal (α−y−G)-contractive via orthogonal metric spaces. We give an application to strengthen our main results from the existing literature to prove the existence of a unique analytical solution to the differential equation by converting it into an integral equation through fixed point analysis.