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A note on stability of the popoviciu functional equation on restricted domain

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EN
Abstrakty
EN
We prove the Hyers-Ulam stability, on restricted domain, of a functional equation of Jensen type, introduced by T. Popoviciu (1965).
Wydawca
Rocznik
Strony
635--641
Opis fizyczny
Bibliogr. 23 poz.
Twórcy
autor
  • Department of Mathematics Pedagogical University Podchorążych 2 30-084 Kraków, Poland, jbrzdek@ap.krakow.pl
Bibliografia
  • [1] T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64–66.
  • [2] D. G. Bourgin, Approximately isometric and multiplicative transformations on continuous function rings, Duke Math. J. 16 (1949), 385-397.
  • [3] D. G. Bourgin, Classes of transformations and bordering transformations, Bull. Amer. Math. Soc. 57 (1951), 223–237.
  • [4] J. Brzdęk, A. Pietrzyk, A note on stability of the general linear equation, Aequationes Math. 75 (2008), 267–270.
  • [5] S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, London, 2002.
  • [6] G. L. Forti, Hyers–Ulam stability of functional equations in several variables, Aequa-tiones Math. 50 (1995), 143-190.
  • [7] G. L. Forti, Comments on the core of the direct method for proving Hyers–Ulam stability of functional equations, J. Math. Anal. Appl. 295 (2004), 127–133.
  • [8] A. Giáyi, Z. Kaiser, Z. Palés, Estimates to the stability of functional equations, Aequationes Math. 73 (2007), 125–143.
  • [9] P. Găvruţa, A generalization of the Hyers–Ulam–Rassias stability of approximately additive mappings, J. Math. Anal. Appl. 184 (1994), 431–436.
  • [10] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
  • [11] D. H. Hyers, G. Isac, Th. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäser, Boston - Basel - Berlin, 1998.
  • [12] S.-M. Jung, Hyers–Ulam–Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, FL, 2001.
  • [13] Z. Moszner, Sur la stabilité de l’équation d’homomorphism, Aequationes Math. 29 (1985), 290-306.
  • [14] Z. Moszner, Sur les définitions différentes de la stabilité des équations fonctionnelles, Aequationes Math. 68 (2004), 260–274.
  • [15] A. Pietrzyk, Stability of the Euler-Lagrange-Rassias functional equation, Demonstratio Math. 39 (2006), 523–530.
  • [16] T. Popoviciu, Sur certaines inégalités qui caractérisentes fonctions convexes, An. Stiinţt. Univ. “Al. I. Cuza” Iasi Secţ. I a Mat. 11 (1965), 155–164.
  • [17] Gy. Pólya, G. Szegö, Aufgaben und Lehrsätze aus der Analysis, vol. I, Springer, Berlin, 1925.
  • [18] Th. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297–300.
  • [19] Th. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Appl. Math. 62 (2000), 23–130.
  • [20] W. Smajdor, Note on a Jensen type functional equation, Publ. Math. Debrecen 63 (2003), 703–714.
  • [21] T. Trif, Hyers–Ulam–Rassias stability of a Jensen type functional equation, J. Math. Anal. Appl. 250 (2000), 579–588.
  • [22] T. Trif, On the stability of the Popoviciu functional equation on bounded domains, In: Stability of Functional Equations of Ulam–Hyers–Rassias Type (ed. S. Czerwik), Hadronic Press, Palm Harbor, 2003, 173–180.
  • [23] S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York, 1960. Reprinted as: Problems in Modern Mathematics, John Wiley & Sons, Inc., New York, 1964.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0032-0021
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