# On the stability of a sum form functional equation related to entropies of type ($\alpha,\beta$)

Volume 14, Issue 3, pp 168--180
Publication Date: November 19, 2020 Submission Date: July 15, 2020 Revision Date: October 18, 2020 Accteptance Date: October 22, 2020
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### Authors

Dhiraj Kumar Singh - Department of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India. Shveta Grover - Department of Mathematics, University of Delhi, Delhi 110007, India.

### Abstract

In this paper, we discuss the stability of the sum form functional equation $\sum\limits _{i=1}^{n}\sum\limits _{j=1}^{m}f(p_{i} q_{j} ) =\sum\limits _{i=1}^{n}g(p_{i}) \sum\limits _{j=1}^{m}f(q_{j} )+\sum\limits _{i=1}^{n}f(p_{i}) \sum\limits _{j=1}^{m}q_{j}^{\beta }$ for all complete probability distributions $(p_1,\ldots,p_n)\in \Gamma_n$, $(q_1,\ldots,q_m)\in \Gamma_m$, $n\ge 3$, $m\ge 3$ are fixed integers, $f$, $g$ are real valued mappings each having the domain $I=[0,1]$ and $\beta$ is a fixed positive real power such that $\beta \neq 1$, $0^\beta:=0$, $1^\beta:=1$.

### Share and Cite

##### ISRP Style

Dhiraj Kumar Singh, Shveta Grover, On the stability of a sum form functional equation related to entropies of type ($\alpha,\beta$), Journal of Nonlinear Sciences and Applications, 14 (2021), no. 3, 168--180

##### AMA Style

Singh Dhiraj Kumar, Grover Shveta, On the stability of a sum form functional equation related to entropies of type ($\alpha,\beta$). J. Nonlinear Sci. Appl. (2021); 14(3):168--180

##### Chicago/Turabian Style

Singh, Dhiraj Kumar, Grover, Shveta. "On the stability of a sum form functional equation related to entropies of type ($\alpha,\beta$)." Journal of Nonlinear Sciences and Applications, 14, no. 3 (2021): 168--180

### Keywords

• Stability
• logarithmic mapping
• multiplicative mapping
• bounded mapping
• entropies of type $(\alpha,\beta)$

•  39B52
•  39B82

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