Fixed point results in incomplete metric spaces for orthogonality-preserving generalized Meir-Keeler $\alpha$-contractive mappings

Olfatian Gillan, Behrooz

doi:‎10.22034/maco.6.1.8

Fixed point results in incomplete metric spaces for orthogonality-preserving generalized Meir-Keeler $\alpha$-contractive mappings

Articles in Press

Document Type : Original Article

Author

Behrooz Olfatian Gillan

Faculty of Basic and Applied Sciences, Kermanshah University of Technology, Kermanshah, Iran.

‎10.22034/maco.6.1.8

Abstract

‎In this paper‎, ‎using the orthogonality concept in an orthogonal metric space‎,
‎we establish the existence and uniqueness of common fixed points for a pair of self-mappings $f$ and $g$ under suitable orthogonality-preserving and orthogonality-reflecting assumptions‎.
‎We show that if $f$ is a continuous orthogonality reflecting self-map of an $O$-$B$-complete metric space $(X,\perp‎ ,‎d)$ (not necessarily a complete metric space)‎, ‎then every orthogonally generalized $\alpha$-$f$-Meir--Keeler contractive map admits a unique common fixed point with $f$‎. ‎Finally‎, ‎as a corollary‎, ‎we show that the classical generalized $\alpha$-$f$-Meir--Keeler contractive condition can be recovered as a particular case of an orthogonal framework‎.

Keywords

fixed point‎, ‎orthogonal metric space‎, ‎orthogonally Meir-Keeler $\alpha$-contractive mapping‎, ‎$\perp$-preserving mapping

Subjects