On Generalized (α‐ψ)‐Contraction With Rational Contraction Type on Generalized Metric Space Endowed With the Orthogonal Direct Sum

This paper explores fixed point theory, focusing on (α‐ψ)‐contraction‐type operators defined on complete generalized metric spaces with an orthogonal direct sum structure. It establishes existence and uniqueness results under these extended contraction conditions. The study further derives new fixed point theorems inspired by and extending the frameworks of Dass–Gupta and Jaggi contractions, contextualizing them within generalized metric spaces with direct sum decompositions. By examining the interplay between the functions α and ψ, these results contribute to a unified theory that bridges and generalizes various contractivity concepts previously studied in metric spaces.