CHARACTERIZATIONS OF POLYNOMIALS WITH MEAN-VALUE PROPERTIES

Authors
CHUNG JK SAHOO PK
Citation
Jk. Chung et Pk. Sahoo, CHARACTERIZATIONS OF POLYNOMIALS WITH MEAN-VALUE PROPERTIES, Applied mathematics letters, 6(3), 1993, pp. 97-100
Citations number
6
Categorie Soggetti
Mathematics,Mathematics
Journal title
Applied mathematics letters → ACNP
ISSN journal
08939659
Volume
6
Issue
3
Year of publication
1993
Pages
97 - 100
Database
ISI
SICI code
0893-9659(1993)6:3<97:COPWMP>2.0.ZU;2-Y
Abstract
We show that if a Lebesgue-integrable function f : R --> R satisfies t he functional equation f [x1, x2,...,x(n)] = h(x1 + x2 + ...+ x(n)), t hen f is a polynomial of degree at most n. This answers a question rai sed by Bailey [1]. Furthermore, we give two other (but related) charac terizations of polynomials.