On a Pexider-type functional equation for quasideviation means. (English) Zbl 0641.39005
The equation
\[
K_{mn}(x_ 1y_ 1,...,x_ my_ 1,...,x_ 1y_ n,...,x_ my_ n)=M_ m(x_ 1,...,x_ m)N_ n(y_ 1,...,y_ n)\quad (x_ 1,...,x_ m,y_ 1,...,y_ n>0)
\]
is solved for quasideviation means [see the author’s definition in Acta Math. Acad. Sci. Hungar. 40, 243-260 (1982; Zbl 0541.26006)]. The solutions correspond to those found by Z. Daróczy and the reviewer [Publ. Math., Debrecen 10, 171-190 (1964; Zbl 0147.312)], under considerably stronger conditions.
Reviewer: J.Aczél
MSC:
| 39B62 | Functional inequalities, including subadditivity, convexity, etc. |
| 94A17 | Measures of information, entropy |
Keywords:
Pexider-type functional equation; deviation; quasideviation; quasiarithmetic; reflexive; symmetric; internal means; probability distributions; continuous; monotonic; multiplicative functions; weights; extension; Shannon entropyReferences:
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