ON A FUNCTIONAL-EQUATION CONNECTED WITH RAO QUADRATIC ENTROPY

Authors
CHUNG JK EBANKS BR NG CT SAHOO PK
Citation
Jk. Chung et al., ON A FUNCTIONAL-EQUATION CONNECTED WITH RAO QUADRATIC ENTROPY, Proceedings of the American Mathematical Society, 120(3), 1994, pp. 843-848
Citations number
4
Categorie Soggetti
Mathematics, General",Mathematics
Journal title
Proceedings of the American Mathematical Society → ACNP
ISSN journal
00029939
Volume
120
Issue
3
Year of publication
1994
Pages
843 - 848
Database
ISI
SICI code
0002-9939(1994)120:3<843:OAFCWR>2.0.ZU;2-1
Abstract
We determine the general solution of the functional equation f(x+y/2)f(x-y/2) = 2f(x/2)+2f(y/2) + lambdaf(x)f(y), for f : [-1, 1] --> R. Th is equation was used by Lau in order to characterize Rao's quadratic e ntropies. The general solution is obtained here as a special case of a mom general result for f mapping a neighborhood of 0 in a linear topo logical space into a field.