Sahil Arora - Department of Mathematics, K.R.M.D.A.V. College, Nakodar, Punjab, ۱۴۴۰۴۰, India
Monika Masta - Department of Mathematics, Om Sterling Global University, Hisar, Haryana, ۱۲۵۰۰۱, India
Mahender Poonia - Department of Mathematics, Om Sterling Global University, Hisar, Haryana, ۱۲۵۰۰۱, India

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.

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