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.


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