Orthogonal stability of the Cauchy functional equation on balls in normed linear spaces

• Autorzy: Sikorska J.
• Języki publikacji: EN

Abstrakty

EN

We study the stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are denned on a finite-dimensional normed linear space with Birkhoff-James orthogonality and take their values in a real sequentially complete linear topological space. The main results establish the stability of the corresponding conditional Cauchy functional equation on a half-ball and in uniformly convex spaces on a whole ball. The methods used in the first part of the paper are similar to those from [10]. Since, however, now in a general structure, some additional problems arise, we need several new tools.

Słowa kluczowe

EN

stability; quadratic mappings; Birkhoff-James orthogonality; Cauchy funntional equation; orthogonal additivity

PL

ortogonalność Birkhoffa-Jamesa; równanie Cauchy'ego

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 3
• Strony: 579--596
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Sikorska J.

• Institute of Mathematics, Silesian University, Bankowa 14, 40-007 Katowice, Poland

Bibliografia

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