Metric conditions, graphic contractions and weakly Picard operators
DOI:
https://doi.org/10.24193/subbmath.2025.1.11Keywords:
Metric space, generalized metric space, contraction type mapping, metric condition, graphic contraction, successive approximation, Picard mapping, pre-weakly Picard mapping, weakly Picard mapping, interpolative Hardy-Rogers mapping, well-posedness of fixed point problem, Ulam-Hyers stability, Ostrowski propertyAbstract
In the paper of S. Park (Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces, Adv. Theory Nonlinear Anal. Appl., 7(2023), No. 2, 455-472), the author solves the following problem: Which metric conditions imposed on f imply that f is a graphic contraction? In this paper we study the following problem: Which metric conditions imposed on f imply that f satisfies the conditions of Rus saturated principle of graphic contractions?
Mathematics Subject Classification (2010): 54H25, 47H10, 54C60.
Received 23 October 2023; Accepted 11 March 2024.
References
[1] Agarwal, R.P., Jleli, M., Samet, B., Fixed-point Theory in Metric spaces, Springer, 2018.
[2] Berinde, V., Iterative Approximation of Fixed-points, Springer-Verlag Heidelberg Berlin, 2007.
[3] Berinde, V., Petrușel, A., Rus, I.A., Remarks on the terminology of the mappings in fixed-point iterative methods in metric spaces, Fixed Point Theory, 24(2023), No. 2, 525-540.
[4] Filip, A.-D., Fixed-point Theory in Kasahara Spaces, Casa Cărții de Știință, Cluj-Napoca, 2015.
[5] Filip, A.-D., Fixed-point theorems for nonself generalized contractions on a large Kasahara space, Carpathian J. Math., 38(2022), No. 3, 799-809.
[6] Hardy, G.E., Rogers, T.D., A generalization of a fixed-point theorem of Reich, Canad. Math. Bull., 16(1973), 201-206.
[7] Karapinar, E., Agarwal, R., Aydi, H., Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6(2018) 256.
[8] Khojasteh, F., Abbas, M, Costache, S., Two new types of fixed-point theorems in complete metric spaces, Abstr. Appl. Anal., 2014, Art. ID 325840, 5pp.
[9] Kirk, W.A., Sims, B., (eds.), Handbook of Metric Fixed Point Theory, Kluwer, 2001.
[10] Park, S., Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces, Adv. Theory Nonlinear Anal. Appl., 7(2023), No. 2, 455-472.
[11] Petrușel, A., Rus, I.A., Graphic contraction principle and application, In: Th. Rassis et al. (eds.), Mathematical Analysis and Application, Springer, 2019, 395-416.
[12] Rhoades, B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226(1977), 257-290.
[13] Rus, I.A., On common fixed-points, Stud. Univ. Babeș-Bolyai Math., 18(1973), 31-33.
[14] Rus, I.A., Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.
[15] Rus, I.A., Relevant classes of weakly Picard operators, An. Univ. Vest Timișoara, Mat.-Inform., 54(2016), no. 2, 3-19.
[16] Rus, I.A., Some variants of contraction principle, generalizations and applications, Stud. Univ. Babeș-Bolyai Math., 61(2016), No. 3, 343-358.
[17] Rus, I.A., Around metric coincidence point theory, Stud. Univ. Babeș-Bolyai Math.,
68(2023), No. 2, 449-463.
[18] Rus, I.A., Petrușel, A., Petrușel, G., Fixed-point Theory, Cluj University Press, Cluj-Napoca, 2008.
[19] Rus, I.A., Șerban, M.-A., Basic problems of the metric fixed-point theory, Carpathian J. Math., 29(2013), 239-258.
[20] Tongnoi, B., Saturated versions of some fixed-point theorems for generalized contractions, Fixed-point Theory, 21(2020), No. 2, 755-766.
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