http://hdl.handle.net/20.500.12128/15962
Title: | Orthogonal stability of the Cauchy functional equation on balls in normed linear spaces |
Authors: | Sikorska, Justyna |
Keywords: | orthogonal stability; Cauchy functional equation; linear spaces |
Issue Date: | 2004 |
Citation: | Demonstratio Mathematica, Vol. 37, nr 3 (2004) s. 579-596 |
Abstract: | We study the 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 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. |
URI: | http://hdl.handle.net/20.500.12128/15962 |
DOI: | 10.1515/dema-2004-0309 |
ISSN: | 2391-4661 0420-1213 |
Appears in Collections: | Artykuły (WNŚiT) |
File | Description | Size | Format | |
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Sikorska_Orthogonal_stability_of_the_Cauchy.pdf | 1,63 MB | Adobe PDF | View/Open |
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