Geodesic
Bounded Solutions of a Functional Inequality
Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 491-495

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DOI

It is known that if f is a real valued function on a rational vector space V, δ > 0, 1 and if f is unbounded then f(x + y) = f(x)f(y) for all x, y ∊ V. In response to a problem of E. Lukacs, in this paper we study the bounded solutions of (1). For example, it is shown that if f is a bounded solution of (1) then - δ ≤ f(x) ≤ (1 + (1 + 4δ)1/2)/2 for all x ∊ V and these bounds are optimal.
DOI : 10.4153/CMB-1982-071-9
Mots-clés : 39C05, 26D99, 39B20 
Albert, Michael; Baker, John A. Bounded Solutions of a Functional Inequality. Canadian mathematical bulletin, Tome 25 (1982) no. 4, pp. 491-495. doi: 10.4153/CMB-1982-071-9
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     title = {Bounded {Solutions} of a {Functional} {Inequality}},
     journal = {Canadian mathematical bulletin},
     pages = {491--495},
     year = {1982},
     volume = {25},
     number = {4},
     doi = {10.4153/CMB-1982-071-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1982-071-9/}
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