On subadditive functions and ψ-additive mappings
Janusz Matkowski
Open Mathematics, Tome 1 (2003), p. 435-440 / Harvested from The Polish Digital Mathematics Library
Access to full text
Full (PDF)

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

Publié le : 2003-01-01
EUDML-ID : urn:eudml:doc:268773 
@article{bwmeta1.element.doi-10_2478_BF02475177,
     author = {Janusz Matkowski},
     title = {On subadditive functions and $\psi$-additive mappings},
     journal = {Open Mathematics},
     volume = {1},
     year = {2003},
     pages = {435-440},
     zbl = {1038.39018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475177}
}

Janusz Matkowski. On subadditive functions and ψ-additive mappings. Open Mathematics, Tome 1 (2003) pp. 435-440. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475177/

[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. | Zbl 0078.10004

[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. | Zbl 0844.39015