On the stability of the squares of some functional equations

Authors

  • Zenon Moszner

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

J.A. Baker, The stability of the cosine equation, Proc. Amer. Math. Soc. 80 (1980), no. 3, 411–416.
##plugins.generic.googleScholarLinks.settings.viewInGS##

B. Batko, On the stability of an alternative functional equation, Math. Inequal. Appl. 8 (2005), no. 4, 685–691.
##plugins.generic.googleScholarLinks.settings.viewInGS##

B. Batko, Superstability of the Cauchy equation with squares in finite-dimensional normed algebras, Aequationes Math. 89 (2015), no. 3, 785–789.
##plugins.generic.googleScholarLinks.settings.viewInGS##

P.W. Cholewa, The stability of the sine equation, Proc. Amer. Math. Soc. 88 (1983), no. 4, 631–634.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Zenon Moszner
##plugins.generic.googleScholarLinks.settings.viewInGS##

D.H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A. 27 (1941), 222–224.
##plugins.generic.googleScholarLinks.settings.viewInGS##

D.H. Hyers, S.M. Ulam, On approximate isometries, Bull. Amer. Math. Soc. 51 (1945), 288–292.
##plugins.generic.googleScholarLinks.settings.viewInGS##

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.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Z. Moszner, Sur l’orientation d’un groupe, Tensor (N.S.) 48 (1989), no. 1, 19–20.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Z. Moszner, On stability of some functional equations and topology of their target spaces, Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012), 69–94.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Z. Moszner, On the inverse stability of functional equations, Banach Center Publications 99 (2013), 111–121.
##plugins.generic.googleScholarLinks.settings.viewInGS##

M. Omladič, P. Šemrl, On non linear perturbations of isometries, Math. Ann. 303 (1995), no. 1, 617–628.
##plugins.generic.googleScholarLinks.settings.viewInGS##

W. Żelazko, Algebry Banacha, Biblioteka Matematyczna, Tom 32, PWN, Warsaw, 1968. Cited on 84 and 94. Institute of Mathematics Pedagogical University Podchorążych 2 30-084 Kraków Poland E-mail: zmoszner@up.krakow.pl Received: February 4, 2015; final version: July 22, 2015; available online: September 23, 2015.
##plugins.generic.googleScholarLinks.settings.viewInGS##

Downloads

Published

2015-12-30

How to Cite

Moszner, Z. (2015). On the stability of the squares of some functional equations. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 14, 81–104. Retrieved from https://studmath.uken.krakow.pl/article/view/13156

Issue

Vol. 14 (2015)

Section

Published on-line (DOI inactive)

License

Copyright (c) 2015 Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica

Creative Commons License

This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Most read articles by the same author(s)