Fixed point theorems for generalized orthogonal F-contraction and F-expansion of Wardowski kind via the notion of \psi-fixed point

In this manuscript, we introduce generalized orthogonal (\mathfrak{f^{*}}, \psi)-contraction of kind (S) and use this concept to establish \psi-fixed point theorems in the frame of O-complete orthogonal metric space. Secondly, we introduce the new notion of generalized orthogonal (\mathfrak{f^{*}}, \psi) expansive mapping and utilize the same to prove some fixed point results for surjective mapping satisfying certain conditions. Our results extend and improve the results of  [۳] and [۷] by omitting the continuity condition of F\in \Im with the aid of \psi-fixed point. We also give an illustrative example which yields the main result. Also, many existing results in the frame of metric spaces are established.

Keywords:

Generalized orthogonal (\mathfrak{f^{*}} , \psi)-contraction , Generalized orthogonal (\mathfrak{f^{*}} , \psi)-expansion , \psi-fixed point , \perp-preserving function , \perp-continuous function , Lower semi-continuous function