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

Arora, Sahil

doi:10.22075/ijnaa.2022.24588.2780

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

Document Type : Research Paper

Author

Sahil Arora

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

10.22075/ijnaa.2022.24588.2780

Abstract

In this manuscript, we introduce generalized ($\mathfrak{f^{*}},\psi)$-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($\mathfrak{f^{*}}, \psi)$ 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 $F\in \Im$ 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