Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: Cauchy equation

Sortuj według:

Ogranicz wyniki do:

Stability of the Cauchy equation in F-norms

Siudut S.

Opuscula Mathematica

2002

Vol. 22

27-34

The subject of this paper is the stability of the Cauchy functional equation f(x · y) = f(x) + f(y) on a semigroup S. A criterion for the Cauchy equation to be stable is proved. Some applications of the criterion are given. In particular, we will strengthen a theorem by Jacek Tabor by removing the assumption that the centre of S is nonempty. This theorem concerns the stability of the Cauchy equation in the Lipschitz norms.

Przedmiotem tej pracy jest stabilność równania funkcyjnego Cauchy'ego f(x · y) = f(x) + f(y) na półgrupie S [...]. Udowodnimy pewne kryterium stabilności równania Cauchy'ego i podamy kilka zastosowań tego kryterium. W szczególności, wzmocnimy pewne twierdzenie Jacka Tabora, usuwając zbędne założenie o niepustości centrum S. Twierdzenie to dotyczy stabilności równania Cauchy'ego w normach Lipschitza.

On conditional Jensen equation

Ziółkowski M.

Demonstratio Mathematica

2001

Vol. 34, nr 4

810-818

Orthogonal stability of the Cauchy equation on balls

Sikorska J.

Demonstratio Mathematica

2000

Vol. 33, nr 3

527-546

We deal with stability of some functional equations postulated for orthogonal vectors in a ball centered at the origin. The maps considered are defined on a finite dimensional inner product space and take their values in a real sequentially complete linear topological space. The main result establishes the stability of the corresponding conditional Cauchy functional equation and as a consequence we obtain some other stability resuits. Results which do not involve the orthogonality relation are considered in more general structures.

On the stability of the Gauss equation

Bil A.

Demonstratio Mathematica

1998

Vol. 31, nr 4

841-848

The stability of the Gauss functional equation (1) is proved. The stability considered here is in a sense analogous to that examined by Th. M. Rassias [4] and Z. Gajda [3] in connection with the Cauchy functional equation.