Superstability of Generalized Multiplicative Functionals
<p/> <p>Let <inline-formula> <graphic file="1029-242X-2009-486375-i1.gif"/></inline-formula> be a set with a binary operation <inline-formula> <graphic file="1029-242X-2009-486375-i2.gif"/></inline-formula> such that, for each <i...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/486375 |
| Summary: | <p/> <p>Let <inline-formula> <graphic file="1029-242X-2009-486375-i1.gif"/></inline-formula> be a set with a binary operation <inline-formula> <graphic file="1029-242X-2009-486375-i2.gif"/></inline-formula> such that, for each <inline-formula> <graphic file="1029-242X-2009-486375-i3.gif"/></inline-formula>, either <inline-formula> <graphic file="1029-242X-2009-486375-i4.gif"/></inline-formula>, or <inline-formula> <graphic file="1029-242X-2009-486375-i5.gif"/></inline-formula>. We show the superstability of the functional equation <inline-formula> <graphic file="1029-242X-2009-486375-i6.gif"/></inline-formula>. More explicitly, if <inline-formula> <graphic file="1029-242X-2009-486375-i7.gif"/></inline-formula> and <inline-formula> <graphic file="1029-242X-2009-486375-i8.gif"/></inline-formula> satisfies <inline-formula> <graphic file="1029-242X-2009-486375-i9.gif"/></inline-formula> for each <inline-formula> <graphic file="1029-242X-2009-486375-i10.gif"/></inline-formula>, then <inline-formula> <graphic file="1029-242X-2009-486375-i11.gif"/></inline-formula> for all <inline-formula> <graphic file="1029-242X-2009-486375-i12.gif"/></inline-formula>, or <inline-formula> <graphic file="1029-242X-2009-486375-i13.gif"/></inline-formula> for all <inline-formula> <graphic file="1029-242X-2009-486375-i14.gif"/></inline-formula>. In the latter case, the constant <inline-formula> <graphic file="1029-242X-2009-486375-i15.gif"/></inline-formula> is the best possible.</p> |
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| ISSN: | 1025-5834 1029-242X |