| 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:
|
http://hdl.handle.net/10338.dmlcz/134650 |
| . |
| Reference:
|
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| . |
