On some qualitative properties of Ćirić's fixed point theorem
DOI:
https://doi.org/10.24193/subbmath.2022.1.04Keywords:
Metric space, fixed point, Ćirić type operator, graphic contraction, data dependence, Ostrowski stability, Ulam-Hyers stability, well-posedness.Abstract
It is well known that of all the extensions of the Banach-Caccioppoli Contraction Principle, the most general result was established by Ćirić in 1974. In this paper, we will present some results related to Ćirić 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).
Mathematics Subject Classification (2010): 47H10, 54H25.
Received 02 November 2021; Revised 18 November 2021; Accepted 19 November 2021.
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