Fixed-point results for convex orbital operators

• Autorzy: Popescu Ovidiu

Identyfikatory

DOI

10.1515/dema-2022-0184

• Języki publikacji: EN

Abstrakty

EN

The aim of this article is to introduce a new type of operator similar to those of A. Petruşel and G. Petruşel type (Fixed point results for decreasing convex orbital operators, J. Fixed Point Theory Appl. 23 (2021), no. 35) and prove some fixed-point theorems which generalize and complement several results in the theory of nonlinear operators.

Słowa kluczowe

EN

Hilbert space; graphic contraction; convex orbital Lipschitz operator; weakly Picard operator; fixed-point

PL

przestrzeń Hilberta; operatory Picarda; punkt stały

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2023
• Tom: Vol. 56, nr 1
• Strony: art. no. 20220184
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Popescu Ovidiu

• Department of Mathematics and Computer Sciences, Transilvania University of Braşov, Braşov, Romania

Bibliografia

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• [2] S. Reich and A. J. Zaslavski, Well-posedness of fixed-point problems, East J. Math. Sci. Special Volume (Functional Analysis and its Applications), Part III, (2001), 393–401.
• [3] S. Reich and A. J. Zaslavski, Genericity in Nonlinear Analysis, Springer, New York, 2014.
• [4] A. M. Ostrowski, The round off stability of iterations, Z. Angew. Math. Mech. 47 (1967), 77–81.
• [5] I. A. Rus and M. A. Şerban, Basic problems of the metric fixed-point theory and the relevance of a metric fixed-point theorem, Carpathian J. Math. 29 (2013), 239–258.
• [6] I. A. Rus, Results and problems in Ulam stability of operatorial equations and inclusions, in: T. Rassias (ed.) Handbook of Functional Equations, Springer, New York, 2014.
• [7] I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory 10, (2009), 305–320.
• [8] A. Petruşel and I. A. Rus, Graphic contraction principle and applications, In: T. M. Rassias, P. M. Pardalos (eds.), Mathematical Analysis and Applications, Springer, Cham, 2019.
• [9] A. Petruşel and G. Petruşel, Fixed point results for decreasing convex orbital operators, J. Fixed Point Theory Appl. 23 (2021), no. 35.
• [10] V. Berinde and M. Păcurar, Approximating fixed-points of enriched contractions in Banach spaces, J. Fixed Point Theory Appl. 22 (2020), no. 38.
• [11] Lj. B.Ciric, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc. 45 (1974), 267–273.
• [12] W. A. Kirk and B. Sims (eds.), Handbook of Metric Fixed Point Theory, Kluwer Academic Publishers, Dordrecht, 2001.
• [13] S. Reich, Some remarks concerning contractions mappings, Can. Math. Bull. 14 (1971), 121–124.
• [14] S. Reich, Fixed point of contractive functions, Boll. Un. Mat. Ital. 5 (1972), 26–42.
• [15] I. A. Rus, A. Petruşel, and G. Petruşel, Fixed Point Theory, Cluj University Press, Cluj-Napoca, 2008.
• [16] E. Llorens-Fuster, Partially nonexpansive mappings, Adv. Theory Nonlinear Analysis Appl. 6 (4) (2002), 565–573.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).