Summary.
We consider the different notions of unique or not unique stability of functional equations and of conditional functional equations and we give some examples and remarks on this subject.
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Manuscript received: January 28, 2004 and, in final form, June 7, 2004.
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Moszner, Z. Sur les définitions différentes de la stabilité des équations fonctionnelles. Aequationes Math. 68, 260–274 (2004). https://doi.org/10.1007/s00010-004-2749-3
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DOI: https://doi.org/10.1007/s00010-004-2749-3
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Keywords.
- Équation fonctionnelle et équation fonctionnelle conditionnelle (functional equation and conditional functional equation) : stable (stable)
- stable uniquement (uniquely stable)
- stable non-uniquement (not uniquely stable)
- stable totalement non-uniquement (totally not uniquely stable)
- b-stable uniquement (uniquely b-stable)
- b-stable non-uniquement (not uniquely b-stable)
- b-stable uniformément (uniformly b-stable)
- b-stable uniformément et uniquement (uniformly and uniquely b-stable)
- b-stable uniformément non-uniquement (uniformly not uniquely b-stable)
- stable fortement (strongly stable)
- stable fortement et uniquement (strongly and uniquely stable)
- stable fortement non-uniquement (strongly not uniquely stable)
- stable itérativement (iteratively stable)
- stable itérativement et uniquement (iteratively and uniquely stable)
- stable itérativement non-uniquement (iteratively not uniquely stable)
- stable itérativement totalement non-uniquement (iteratively totally not uniquely stable)
- superstable (superstable)
- superstable fortement (strongly superstable)
- stable complètement (completely stable)