Twisted $(\alpha,\beta)$-Contractive Mapping with Preserving Orthogonality and Hyers-Ulam Stability

Abstract

‎‎In his study‎, ‎we define $\alpha$-$\psi$-contractive type mapping‎, ‎twisted $(\alpha,\beta)$-admissible mapping‎, ‎and twisted $(\alpha,\beta)$-contractive mapping on orthogonally metric space‎. ‎After that‎, ‎we will examine the fixed point theorem for $\alpha$-$\psi$-contractive mappings with preserving orthogonality‎. ‎For instance‎, ‎we demonstrate that there is an orthogonally fixed point for orthogonally $\alpha$-$\psi$-contractive type mapping‎, ‎but under these conditions‎, ‎it does not exist in the metric space‎. ‎Next‎, ‎we set up a common fixed point with orthogonally preserving for new concepts defined under different conditions in an orthogonally metric space‎. ‎Moreover‎, ‎we demonstrate through an example that a fixed point with orthogonally preserving exists for new concepts defined under different conditions‎. ‎Lastly‎, ‎we show that the defined concepts can be stable‎