Document Type : Research Paper

Authors

• Sahil Arora ¹
• Monika Masta ²
• Mahender Poonia ²

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 (${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$-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 (${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$ 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 $F\in \mathrm{\Im }$ 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 (${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$-contraction
• Generalized orthogonal (${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$-expansion, $\psi$-fixed point, $\perp$-preserving function, $\perp$-continuous function, Lower semi-continuous function