On some qualitative properties of Ciric's fixed point theorem

Abstract

"It is well known that of all the extensions of the Banach-Caccioppoli Contraction Principle, the most general result was established by \'{C}iri\'{c} in 1974. In this paper, we will present some results related to \'{C}iri\'{c} type operator in complete metric spaces. Existence and uniqueness are re-called and several stability properties (data dependence and Ostrowski stability property) are proved. Using the retraction-displacement condition, we will establish the well-posedness and the Ulam-Hyers stability property of the fixed point equation $x=f(x)$."