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

Singh, Dhiraj Kumar ¹ ; Grover, Shveta ²

¹ Department of Mathematics, Zakir Husain Delhi College (University of Delhi), Jawaharlal Nehru Marg, Delhi 110002, India
² Department of Mathematics, University of Delhi, Delhi 110007, India

Journal of nonlinear sciences and its applications, Tome 14 (2021) no. 3, p. 168-180.

Résumé

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 $\beta \neq 1$, $0^\beta:=0$, $1^\beta:=1$.

Détail

DOI : 10.22436/jnsa.014.03.06

Classification : 39B52, 39B82
Keywords: Stability, additive mapping, logarithmic mapping, multiplicative mapping, bounded mapping, entropies of type \((\alpha,\beta)\)

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