Fischer-Muszély functional equation almost everywhere
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| 003 | CHVBK | ||
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| 008 | 210128e20150201xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00010-014-0299-x |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00010-014-0299-x | ||
| 100 | 1 | |a Ger |D Roman |u Institute of Mathematics, Silesian University, ul. Bankowa 14, PL-40-007, Katowice, Poland |4 aut | |
| 245 | 1 | 0 | |a Fischer-Muszély functional equation almost everywhere |h [Elektronische Daten] |c [Roman Ger] |
| 520 | 3 | |a We show that, under suitable assumptions, a function f from a group (G, +) into a real or complex inner product space $${(H, (\cdot \vert \cdot))}$$ ( H , ( · | · ) ) , satisfying the Fischer-Muszély functional equation $$\parallel f(x + y)\parallel\, \, =\, \parallel f(x) + f(y)\parallel$$ ‖ f ( x + y ) ‖ = ‖ f ( x ) + f ( y ) ‖ for all pairs (x, y) off a sufficiently small (negligible) subset of G 2 has to be almost everywhere equal to an additive map from G into H, i.e. the set $${\{x \in G: f(x) \neq a(x)\}}$$ { x ∈ G : f ( x ) ≠ a ( x ) } is small (negligible) in G. Small sets in G and G 2 are defined in an axiomatic way. Several corollaries illustrating some consequences of this result are presented. | |
| 540 | |a The Author(s), 2014 | ||
| 690 | 7 | |a Fischer-Muszély equation |2 nationallicence | |
| 690 | 7 | |a p.l.i. ideal |2 nationallicence | |
| 690 | 7 | |a conjugate ideals |2 nationallicence | |
| 690 | 7 | |a equality (equation) valid $${\mathcal{J}}$$ J -almost everywhere ( $${\Omega(\mathcal{J})}$$ Ω ( J ) -almost everywhere) |2 nationallicence | |
| 773 | 0 | |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 207-214 |x 0001-9054 |q 89:1<207 |1 2015 |2 89 |o 10 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00010-014-0299-x |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00010-014-0299-x |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 100 |E 1- |a Ger |D Roman |u Institute of Mathematics, Silesian University, ul. Bankowa 14, PL-40-007, Katowice, Poland |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Aequationes mathematicae |d Springer Basel |g 89/1(2015-02-01), 207-214 |x 0001-9054 |q 89:1<207 |1 2015 |2 89 |o 10 | ||