Document Type : Research Paper

Author

• Sahil Arora

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

Abstract

In this manuscript, we introduce generalized (${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$-contraction of kind (S) and use this concept to establish $\psi$-fixed point theorems in the frame of complete metric space. Secondly, we introduce new notion of generalized(${\mathfrak{f}}^{\mathfrak{\ast }},\psi )$ expansive mapping of kind (S) and utilize the same to prove some fixed point results for surjective mapping satisfying certain conditions. Our results improve the results of [8], [10] and [14] by omitting the continuity condition of $F\in \mathrm{\Im }$ with the aid of $\psi$-fixed point. We also give an example which yields the main result. Also, many existing results in the frame of metric spaces are established.

Keywords

• Generalized ($\mathfrak{f^{*}}
• \psi)$-contraction
• Generalized ($\mathfrak{f^{*}}
• \psi)$-expansion
• $\psi$-fixed point
• Lower semi-continuous function