Nonlinear quasicontractions in complete metric spaces

Two essential extensions of the Banach Fixed Point Theorem are due to Lj.B. Ćirić and J. Matkowski. The first author obtained fixed point result for linear quasicontractions, while the second one for nonlinear contractions. The aim of the present note is to give common view of these theorems in the spirit of a contraction principle due to M. Hegedűs and T. Szilágyi.