Published online by Cambridge University Press: 20 November 2018
In this paper, we are concerned with the functional inequality
1
where 0 < Pi < l, 0 < qi < l, fi(p)≠0, for 0 < P < 1, (i = 1, 2,..., n) and n is a fixed positive integer, n ≥ 2.
Inequality (1) was studied by Rényi and Fischer, (see [1], [3]) in the special case
2
and this provided a characterization of Rényi's entropy.