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Functional Analysis and Its Applications

, Volume 50, Issue 1, pp 80–82 | Cite as

On Nearly Subadditive Maps

  • E. V. Shulman
Brief Communications
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Abstract

Several results on stability in spirit of Ulam and Hyers are obtained for classes of maps from groups to lattices satisfying the subadditivity condition
$$F\left( {gh} \right) \subset F\left( g \right) \cup F\left( h \right){\kern 1pt} \;for\;g,h \in G$$
.

Key words

subadditive set-valued maps on groups addition theorems stability problems 

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References

  1. [1]
    D. H. Hyers, Proc. Nat. Acad. Sci. USA, 27 (1941), 222–224.MathSciNetCrossRefGoogle Scholar
  2. [2]
    D. H. Hyers, G. Isac, and T. M. Rassias, Stability of Functional Equations in Several Variables, Progress in Nonlinear Differential Equations and their Applications, vol. 34, Birkhäuser, Boston, MA, 1998.CrossRefMATHGoogle Scholar
  3. [3]
    E. Shulman, J. Funct. Anal., 263:5 (2012), 1468–1484.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Vologda State UniversityVolgogradRussia

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