On the general solution of a functional equation connected to sum form information measures on open domain. III
type: Item
instance of: scholarly article
title: On the general solution of a functional equation connected to sum form information measures on open domain. III
zbMATH Open document ID: 0628.39009
DOI: 10.1155/S0161171286000686
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/46223
review text: [For part I see Publ. Inst. Math., Nouv. Ser. 40(54), 57-62 (1986; Zbl 0619.39009).] This paper is devoted to the study of a functional equation connected with the characterization of weighted entropy and weighted entropy of degree \(\beta\). Here, we find the general solution of the functional equation \[ \sum^{n}_{i=1}\sum^{m}_{j=1}f(p_ iq_ j,u_ iv_ j)=\sum^{n}_{i=1}p_ i^{\alpha}u_ i\cdot \sum^{m}_{j=1}f(q_ i,v_ j)+\sum^{m}_{j=1}q_ j^{\beta}v_ j\cdot \sum^{n}_{j=1}f(p_ i,u_ i) \] on an open domain, without using 0-probability and 1-probability.
Mathematics Subject Classification ID: 39B99
Mathematics Subject Classification ID: 94A17
zbMATH DE Number: 4021790
zbMATH Keywords: sum form information measures
zbMATH Keywords: weighted entropy
zbMATH Keywords: open domain
zbMATH Keywords: general solution
author: Pl. Kannappan
author: Prasanna Sahoo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4021790