Hyers-Ulam stability of Davison functional equation on restricted domains

• Autorzy: Park Choonkil , Tareeghee Mohammad Amin , Najati Abbas , Noori Batool

Identyfikatory

DOI

10.1515/dema-2024-0039

• Języki publikacji: EN

Abstrakty

EN

In this article, we study the Hyers-Ulam stability of Davison functional equation f(xy)+f(x+y)=f(xy+x)+f(y) on some unbounded restricted domains. Using the obtained results, we study an interesting asymptotic behavior of Davison functions. We also investigate the Hyers-Ulam stability of Davison functional equation and its generalized form given by f(xy)+g(x+y)=h(xy+x)+k(y), for x,y ∈ R⩾0 = {t ∈ R : t ⩾ 0}.

Słowa kluczowe

EN

Hyers-Ulam stability; Davison functional equation; Davison function; asymptotic behavior

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2024
• Tom: Vol. 57, nr 1
• Strony: art. no. 20240039
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Park Choonkil

• Department of Mathematics, Research Institute for Convergence of Basic Science, Hanyang University, Seoul, Korea

autor

Tareeghee Mohammad Amin

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Najati Abbas

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

autor

Noori Batool

• Department of Mathematics, Faculty of Sciences, University of Mohaghegh Ardabili, Ardabil, Iran

Bibliografia

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• [2] W. Benz, 191R1. Remark, Aequationes Math. 20 (1980), 307.
• [3] R. Girgensohn and K. Lajkó, A functional equation of Davison and its generalization, Aequationes Math. 60 (2000), no. 3, 219–224, DOI: https://doi.org/10.1007/s000100050148.
• [4] T. M. K. Davison, A Hosszú-like functional equation, Publ. Math. Debrecen 58 (2001), 505–513, DOI: https://doi.org/10.5486/PMD.2001.2326.
• [5] S. M. Ulam, Problems in Modern Mathematics (Science Editions), John Wiley & Sons, New York, 1964.
• [6] D. H. Hyers, On the stability of the linear functional equation, Proc. Natl. Acad. Sci. USA 27 (1941), 222–224, DOI: https://doi.org/10.1073/pnas.27.4.222.
• [7] D. H. Hyers, G. Isac, and Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser, Basel, 1998.
• [8] S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York, Dordrecht, Heidelberg, London, 2011.
• [9] Pl. Kannappan, Functional Equations and Inequalities with Applications, Springer, New York, 2009.
• [10] S.-M. Jung and P. K. Sahoo, Hyers-Ulam-Rassias stability of an equation of Davison, J. Math. Anal. Appl. 238 (1999), no. 1, 297–304, DOI: https://doi.org/10.1006/jmaa.1999.6545.
• [11] S.-M. Jung and P. K. Sahoo, On the Hyers-Ulam stability of a functional equation of Davison, Kyungpook Math. J. 40 (2000), no. 1, 87–92.
• [12] K.-W. Jun, S.-M. Jung, and Y.-H. Lee, A generalization of the Hyers-Ulam-Rassias stability of a functional equation of Davison, J. Korean Math. Soc. 41 (2004), no. 3, 501–511, DOI: https://doi.org/10.4134/JKMS.2004.41.3.501.
• [13] S.-M. Jung and P. K. Sahoo, Hyers-Ulam-Rassias stability of a functional equation of Davison in rings, Nonlinear Funct. Anal. Appl. 11 (2006), no. 5, 891–896.
• [14] Y.-H. Kim, On the Hyers-Ulam-Rassias stability of an equation of Davison, Indian J. Pure Appl. Math. 33 (2002), 713–726.
• [15] J. Rimán, On an extension of Pexider’s equation, Zb. Rad. (Beogr.) 1 (1976), no. 9, 65–72.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2026).