General solution of two functional equations concerning measures of information. (English) Zbl 0713.39005
A unified method to solve the following functional equations, in the n- dimensional case, is presented.
\[
f(pq)+f(p(1-q))=f(p)(f(q)+f(1-q)),
\]
\[ f(pq)+f(p(1-q))=f(p)(M(q)+M(1-q)) \] (p,q\(\in]0,1[^ n)\). These equations arise in the characterization of multidimensional sum form information measures.
\[ f(pq)+f(p(1-q))=f(p)(M(q)+M(1-q)) \] (p,q\(\in]0,1[^ n)\). These equations arise in the characterization of multidimensional sum form information measures.
Reviewer: P.N.Rathie
References:
| [1] | PL. Kannappan and P.K. Sahoo, Sum form equation of multiplicative type. Acta Math. Acad. Sci. Hungar. Submitted (1989). · Zbl 0674.94005 |
| [2] | Maksa, Gy., The general solution of a functional equation arising in information theory. Acta Math. Acad. Sci. Hungar, 49 (1987), 213–217. · Zbl 0612.39007 · doi:10.1007/BF01956325 |
| [3] | P.K. Sahoo and W. Sander, Sum form information measures on open domain. Radovi Matematicki, 5 (1989), 261–270. · Zbl 0701.39007 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
