Communications of the
Korean Mathematical Society CKMS

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type $F$-contraction and modified TAC-$(\psi,\phi)$-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al.~\cite{du}, Rhoades \cite{rh}, Doric, \cite{doc}, Khan et al.~\cite{kh}, Wardowski \cite{wad}, Piri et al.~\cite{piri}, Sing et al.~\cite{sing} and many more results in this direction.

Keywords: Suzuki mapping, fixed point, TAC-Suzuki Berinde $F$-contraction, TAC-$(\psi,\phi)$-Suzuki type rational contraction, metric space

MSC numbers: 47H09, 47H10, 49J20, 49J40