Wyniki wyszukiwania - BazTech

Ograniczanie wyników

Znaleziono wyników: 4

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: orthogonal additivity

Sortuj według:

Ogranicz wyniki do:

On orthogonally additive injections and surjections

Baron K.

Commentationes Mathematicae

2015

Vol 55, No. 2

157--162

Let E be a real inner product space of dimension at least 2 and V a linear topological Hausdorff space. If card E≤card V, then the set of all orthogonally additive injections mapping E into V is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology. If cardV≤card E, then the set of all orthogonally additive surjections mapping E into V is dense in the space of all orthogonally additive functions from E into V with the Tychonoff topology.

On the stability of orthogonal additivity

Fechner W., Sikorska J.

Bulletin of the Polish Academy of Sciences. Mathematics

2010

Vol. 58, no 1

23-30

We deal with the stability of the orthogonal additivity equation, presenting a new approach to the proof of a 1995 result of R, Ger and the second author. We sharpen the estimate obtained there. Moreover, we work in more general settings, providing an axiomatic framework which covers much more cases than considered before by other authors.

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

Sikorska J.

Demonstratio Mathematica

2004

Vol. 37, nr 3

579--596

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.

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.