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The Hyers–Ulam–Aoki Type Stability of Some Functional Equations on Banach Lattices

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Języki publikacji
EN
Abstrakty
EN
In Agbeko (2012) the Hyers–Ulam–Aoki stability problem was posed in Banach lattice environments with the addition in the Cauchy functional equation replaced by supremum. In the present note we restate the problem so that it relates not only to supremum but also to infimum and their various combinations. We then propose some sufficient conditions which guarantee its solution.
Rocznik
Strony
177--184
Opis fizyczny
Bibliogr. 12 poz.
Twórcy
autor
  • Institute of Mathematics, University of Miskolc, 3515 Miskolc-Egyetemváros, Hungary
Bibliografia
  • [1] N. K. Agbeko, On optimal averages, Acta Math. Hungar. 63 (1994), 133–147.
  • [2] N. K. Agbeko, On the structure of optimal measures and some of its applications, Publ. Math. Debrecen 46 (1995), 79–87.
  • [3] N. K. Agbeko, Stability of maximum preserving functional equations on Banach lattices, Miskolc Math. Notes 13 (2012), 187–196.
  • [4] N. K. Agbeko and S. S. Dragomir, The extension of some Orlicz space results to the theory of optimal measure, Math. Nachr. 286 (2013), 760–771.
  • [5] T. Aoki, Stability of the linear transformation in Banach spaces, J. Math. Soc. Japan 2 (1950), 64–66.
  • [6] W. Fechner, On the Hyers–Ulam stability of functional equations connected with additive and quadratic mappings, J. Math. Anal. Appl. 322 (2006), 774–786.
  • [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] Z. Gajda, On stability of additive mappings, Int. J. Math. Sci. 14 (1991), 431–434.
  • [9] P. Gǎvruţa, On a problem of G. Isac and Th. M. Rassias concerning the stability of mappings, J. Math. Anal. Appl. 261 (2001), 543–553.
  • [10] R. Ger and P. Šemrl, The stability of the exponential equation, Proc. Amer. Math. Soc. 124 (1996), 779–787.
  • [11] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
  • [12] S. M. Ulam, A Collection of Mathematical Problems, Interscience, New York, 1960.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-c70d7cb1-8255-464c-ae27-18c01f7ec058
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