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Title: On a multiplicative type sum form functional equation and its role in information theory (English)
Author: Nath, Prem
Author: Singh, Dhiraj Kumar
Language: English
Journal: Applications of Mathematics
ISSN: 0862-7940 (print)
ISSN: 1572-9109 (online)
Volume: 51
Issue: 5
Year: 2006
Pages: 495-516
Summary lang: English
Category: math
Summary: In this paper, we obtain all possible general solutions of the sum form functional equations \[ \align \sum_{i=1}^{k}\sum_{j=1}^{\ell}f(p_iq_j)=&\sum_{i=1}^{k}g(p_i) \sum_{j=1}^{\ell}h(q_j)\\ \text{and} \sum_{i=1}^{k}\sum_{j=1}^{\ell}F(p_iq_j)=&\sum_{i=1}^{k} G(p_i)+\sum_{j=1}^{\ell}H(q_j)+ \lambda\sum_{i=1}^{k}G(p_i)\sum_{j=1}^{\ell}H(q_j) \endalign \] valid for all complete probability distributions $(p_1,\ldots ,p_k)$, $(q_1,\ldots ,q_\ell )$, $k\ge 3$, $\ell \ge 3$ fixed integers; $\lambda \in \mathbb{R}$, $\lambda \ne 0$ and $F$, $G$, $H$, $f$, $g$, $h$ are real valued mappings each having the domain $I=[0,1]$, the unit closed interval. (English)
Keyword: sum form functional equation
Keyword: additive function
Keyword: multiplicative function
MSC: 39B22
MSC: 39B52
MSC: 39B82
MSC: 94A15
idZBL: Zbl 1164.39330
idMR: MR2261636
DOI: 10.1007/s10492-006-0018-6
Date available: 2009-09-22T18:27:04Z
Last updated: 2020-07-02
Stable URL:
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