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

Document Type : Research Paper

Authors

1 Department of Mathematics, K.R.M.D.A.V. College, Nakodar, Punjab, 144040, India

2 Department of Mathematics, Om Sterling Global University, Hisar, Haryana, 125001, India

Abstract

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  [3] and [7] 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

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###### Volume 14, Issue 2February 2023Pages 221-231
• Receive Date: 14 July 2022
• Revise Date: 07 September 2022
• Accept Date: 11 September 2022