On the stability of the squares of some functional equations

Moszner, Zenon

doi:10.1515/aupcsm-2015-0007

Abstract

We consider the stability, the superstability and the inverse stability of the functional equations with squares of Cauchy’s, of Jensen’s and of isometry equations and the stability in Ulam-Hyers sense of the alternation of functional equations and of the equation of isometry.

References

[1] J.A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411-416. Cited on 93.
Search in Google Scholar
[2] B. Batko, On the stability of an alternative functional equation, Math. Inequal. Appl. 8 (2005), no. 4, 685-691. Cited on 83, 96 and 97.
Search in Google Scholar
[3] B. Batko, Superstability of the Cauchy equation with squares in finite-dimensional normed algebras, Aequationes Math. 89 (2015), no. 3, 785-789. Cited on 82.
Search in Google Scholar
[4] P.W. Cholewa, The stability of the sine equation, Proc. Amer. Math. Soc. 88 (1983), no. 4, 631-634. Cited on 93 and 97.
Search in Google Scholar
[5] D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222-224. Cited on 81.
Search in Google Scholar
[6] D.H. Hyers, S.M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288-292. Cited on 100.
Search in Google Scholar
[7] M. Kuczma, An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality, Second edition. Birkhäuser Verlag, Basel, 2008. Cited on 87.
Search in Google Scholar
[8] Z. Moszner, Sur l’orientation d’un groupe, Tensor (N.S.) 48 (1989), no. 1, 19-20. Cited on 87.
Search in Google Scholar
[9] Z. Moszner, On stability of some functional equations and topology of their target spaces, Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012), 69-94. Cited on 84 and 86.
Search in Google Scholar
[10] Z. Moszner, On the inverse stability of functional equations, Banach Center Publications 99 (2013), 111-121. Cited on 98, 99 and 103.
Search in Google Scholar
[11] M. Omladič, P. Šemrl, On non linear perturbations of isometries, Math. Ann. 303 (1995), no. 1, 617-628. Cited on 100.
Search in Google Scholar
[12] W. Żelazko, Algebry Banacha, Biblioteka Matematyczna, Tom 32, PWN,Warsaw, 1968. Cited on 84 and 94.
Search in Google Scholar

On the stability of the squares of some functional equations

Abstract

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