On the stability of a sum form functional equation related to nonadditive entropies

Volume 23, Issue 4, pp 328--340 http://dx.doi.org/10.22436/jmcs.023.04.06

Publication Date: November 24, 2020 Submission Date: July 16, 2020 Revision Date: September 16, 2020 Accteptance Date: November 03, 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 intend to discuss the stability of \[ \sum\limits^n_{i=1}\sum\limits^m_{j=1}f(p_iq_j)=\sum\limits^n_{i=1}M_1(p_i)\sum\limits^m_{j=1}g(q_j)+\sum\limits^m_{j=1}M_2(q_j)\sum\limits^n_{i=1}h(p_i), \] where \(f:I\to \mathbb R\), \(g:I\to \mathbb R\), \(h:I\to \mathbb R\) are unknown mappings; \(M_1:I\to \mathbb R\), \(M_2:I\to \mathbb R\) are fixed multiplicative mappings both different from identity mapping; \((p_1,\dots,p_n)\in \Gamma_n\), \((q_1,\dots,q_m)\in \Gamma_m\) ; \(n\ge 3\), \(m\ge 3\) are fixed integers.

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Keywords

• Stability
• bounded mapping
• logarithmic mapping
• multiplicative mapping

MSC

•  39B52
•  39B82

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