On some qualitative properties of Ćirić’s fixed point theorem

Madalina Teodora Moga

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).


Keywords


metric space; fixed point; Ćirić type operator; graphic contraction; data dependence; Ostrowski stability; Ulam-Hyers stability; well-posedness

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References


Berinde, V., Măruşter, Şt., Rus, I.A., Saturated contraction principles for non self operators, generalizations and applications, Filomat 31(2017), no. 11, 3391-3406.

Ćirić, Lj. B., A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45(1974), no. 2, 267–273.

Petruşel, A., Ćirić type fixed point theorems, Stud. Univ. Babeş-Bolyai Math. 59(2014), no. 2, 233-245.

Rhoades, B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc. 226(1977), 257–290.

Rus, I.A., Generalized Contractions and Applications, Transilvania Press, Cluj-Napoca, 2001.

Rus, I.A., Relevant classes of weakly Picard operators, Annals of West University of Timişoara - Mathematics and Computer Science, 54(2016), no. 2, 131-147.

Rus, I.A., Some variants of contraction principle, generalizations and applications, Stud. Univ. Babeş-Bolyai Math., 61(2016), no. 3, 343-358.

Rus, I.A., Petruşel, A., Petruşel, G., Fixed Point Theory, Cluj Univ. Press, Cluj-Napoca, 2008.




DOI: http://dx.doi.org/10.24193/subbmath.2022.1.04

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