On subadditive functions and ψ-additive mappings

• Autorzy: Janusz Matkowski
• Języki publikacji: EN

Abstrakty

EN

In [4], assuming among others subadditivity and submultiplicavity of a function ψ: [0, ∞)→[0, ∞), the authors proved a Hyers-Ulam type stability theorem for “ψ-additive” mappings of a normed space into a normed space. In this note we show that the assumed conditions of the function ψ imply that ψ=0 and, consequently, every “ψ-additive” mapping must be additive

Słowa kluczowe

EN

subadditive function; submultiplicative function; Hyers-Ulam stability; ψ-additive function; 39B72

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2003
• Tom: 1
• Numer: 4
• Strony: 435-440

Daty

wydano

2003-12-01

online

2003-12-01

Twórcy

autor

Janusz Matkowski

• University of Zielona Góra

Bibliografia

• [1] P. Gãvruta: “On a problem of G. Isac and Th.M. Rassias concerning the stability of mappings”, J. Math. Anal. Appl., Vol. 261, (2001), pp. 543–553. http://dx.doi.org/10.1006/jmaa.2001.7539
• [2] E. Hille and R.S. Phillips: “Functional analysis and semi-groups”, AMS, Colloquium Publications, Vol. 31, Providence, Rhode Island, 1957.
• [3] G. Isac and Th.M. Rassias: “On the Hyers-Ulam stability of ψ-additive mappings”, J. Approx. Theory, Vol. 72, (1993), pp. 137–137. http://dx.doi.org/10.1006/jath.1993.1010
• [4] G. Isac and Th.M. Rassias: “Functional inequalities for approximately additive mappings”, In: Th.M. Rassias and J. Tabor, (Eds.): Stability of Mappings of Hyers-Ulam type, Hadronic Press, Palm Harbour, Fl, 1994, pp. 117–125.

Identyfikatory

DOI

10.2478/BF02475177