On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings

On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings

In 1940 S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved this problem for linear mappings. According to P. M. Gruber (1978) this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types....

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Bibliographic Details
Published in:Aequationes mathematicae Vol. 64; no. 1-2; pp. 62 - 69
Main Author: Rassias, J. M.
Format: Journal Article
Language:English
Published: Basel Springer Nature B.V 01-08-2002
Subjects:
Algebra
Mapping
Mathematical analysis
Online Access:Get full text
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Summary:In 1940 S. M. Ulam proposed the well-known Ulam stability problem. In 1941 D. H. Hyers solved this problem for linear mappings. According to P. M. Gruber (1978) this kind of stability problems is of particular interest in probability theory and in the case of functional equations of different types. In 1982-1999 we solved the above Ulam problem for different mappings. In this paper we solve the Hyers-Ulam stability problem for quadratic multi-dimensional mappings. [PUBLICATION ABSTRACT]
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-002-8031-7