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


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


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.


Volume 14, Issue 1
January 2023
Pages 495-504
  • Receive Date: 20 September 2021
  • Revise Date: 30 September 2021
  • Accept Date: 05 September 2022