On subadditive functions and ψ-additive mappings

Janusz Matkowski

Open Mathematics (2003)

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

Abstract

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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

How to cite

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Janusz 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

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  1. [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. [2] E. Hille and R.S. Phillips: “Functional analysis and semi-groups”, AMS, Colloquium Publications, Vol. 31, Providence, Rhode Island, 1957. Zbl0078.10004
  3. [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. [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

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