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

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 [۸], [۱۰] and [۱۴] 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