Linear approximation of approximately linear functions

Ulam posed the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In this spirit we investigate the stability (local and global) of Jensen's functional equation and approximate (in the spirit of John) epsilon-rigid maps, epsilon-iso...

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Vydáno v:Aequationes mathematicae Ročník 66; číslo 1-2; s. 37 - 77
Hlavní autor: Vestfrid, Igor A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel Springer Nature B.V 01.08.2003
Témata:
Linear algebra
Mapping
Mathematical functions
Mathematics
Theory
ISSN:0001-9054, 1420-8903
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Shrnutí:Ulam posed the problem: "Give conditions in order for a linear mapping near an approximately linear mapping to exist". In this spirit we investigate the stability (local and global) of Jensen's functional equation and approximate (in the spirit of John) epsilon-rigid maps, epsilon-isometries and epsilon-quasi-isometries by affine near isometries. In this way we extend one of John's theorems. [PUBLICATION ABSTRACT]
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-003-2644-3