On the stability of the squares of some functional equations

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.

Keywords


Stability, superstability, inverse stability, isometry

Mathematics Subject Classification (2010)


39B82; 39B62

References


Baker, J.A. "The stability of the cosine equation." Proc. Amer. Math. Soc. 80.3 (1980): 411–416.

Batko, B. "On the stability of an alternative functional equation." Math. Inequal. Appl. 8.4 (2005): 685–691.

Batko, B. "Superstability of the Cauchy equation with squares in finite-dimensional normed algebras." Aequationes Math. 89.3 (2015): 785–789.

Cholewa, P.W. "The stability of the sine equation." Proc. Amer. Math. Soc. 88.4 (1983): 631–634.

Hyers, D.H. "On the stability of the linear functional equation." Proc. Nat. Acad. Sci. U.S.A. 27 (1941): 222–224.

Hyers, D.H. and S.M. Ulam. "On approximate isometries." Bull. Amer. Math. Soc. 51 (1945): 288–292.

Kuczma, "An introduction to the theory of functional equations and inequalities. Cauchy’s equation and Jensen’s inequality." Second edition. Basel: Birkhäuser Verlag, 2008.

Moszner, Z. "Sur l’orientation d’un groupe." Tensor (N.S.) 48.1 (1989): 19–20.

Moszner, Z. "On stability of some functional equations and topology of their target spaces." Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012): 69–94.

Moszner, Z. "On the inverse stability of functional equations." Banach Center Publications 99 (2013): 111–121.

Omladic, M. and P. Šemrl. "On non linear perturbations of isometries." Math. Ann. 303.1 (1995): 617–628.

Żelazko, W. "Algebry Banacha." Biblioteka Matematyczna, Tom 32. Warsaw: PWN,1968.


Full Text: PDF

Download statistics: 1821

Licencja Creative Commons
This article by Zenon Moszner is governed by the Creative Commons Attribution-ShareAlike 4.0 International(CC BY-SA 4.0) licence.


e-ISSN: 2300-133X, ISSN: 2081-545X

Since 2017 Open Access in De Gruyter and CrossCheck access cofinanced by The Ministry of Science and Higher Education - Republic of Poland - DUN 775/P-DUN/2017 see more

The Journal is indexed in:
and others see Abstracting and Indexing list

AUPC SM is on the List of the Ministry’s scored journals with 20 points for 2019

Deklaracja dostępności cyfrowej