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

Volume 14, Issue 3, pp 168--180 http://dx.doi.org/10.22436/jnsa.014.03.06
Publication Date: November 19, 2020 Submission Date: July 15, 2020 Revision Date: October 18, 2020 Accteptance Date: October 22, 2020

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 \(\beta \neq 1\), \(0^\beta:=0\), \(1^\beta:=1\).


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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


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