# On subadditive functions and ψ-additive mappings

Open Mathematics (2003)

- Volume: 1, Issue: 4, page 435-440
- ISSN: 2391-5455

## Access Full Article

top## Abstract

top## How to cite

topJanusz Matkowski. "On subadditive functions and ψ-additive mappings." Open Mathematics 1.4 (2003): 435-440. <http://eudml.org/doc/268773>.

@article{JanuszMatkowski2003,

abstract = {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},

author = {Janusz Matkowski},

journal = {Open Mathematics},

keywords = {39B72},

language = {eng},

number = {4},

pages = {435-440},

title = {On subadditive functions and ψ-additive mappings},

url = {http://eudml.org/doc/268773},

volume = {1},

year = {2003},

}

TY - JOUR

AU - Janusz Matkowski

TI - On subadditive functions and ψ-additive mappings

JO - Open Mathematics

PY - 2003

VL - 1

IS - 4

SP - 435

EP - 440

AB - 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

LA - eng

KW - 39B72

UR - http://eudml.org/doc/268773

ER -

## References

top- [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. Zbl0078.10004
- [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. Zbl0844.39015

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.