On the stability of a multiplicative type sum form functional equation

In this paper we intend to discuss the stability of a sum form functional equation \begin{align*} \sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}f\left(p_iq_j\right)=\sum\limits\limits^n_{i=1}k\left(p_i\right)\sum\limits\limits^m_{j=1}q^{\beta }_j \end{align*} where f, k are real valued mapping...

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Bibliographic Details
Published in:Ratio mathematica 2021-12, Vol.41, p.7-18
Main Authors: Surbhi Madan, Grover, Shveta, Singh, Dhiraj Kumar
Format: Article
Language:English
Subjects:
additive mapping
bounded mapping
functional equation
Functional equations
Mathematics
Numbers
Stability
stability of a sum form functional equation
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Summary:In this paper we intend to discuss the stability of a sum form functional equation \begin{align*} \sum\limits\limits^n_{i=1}\sum\limits\limits^m_{j=1}f\left(p_iq_j\right)=\sum\limits\limits^n_{i=1}k\left(p_i\right)\sum\limits\limits^m_{j=1}q^{\beta }_j \end{align*} where f, k are real valued mappings each having the domain I; (p_1,\ldots,p_n)∈\Gamma_n, (q_1,\ldots,q_m)\in\Gamma_m; n\ge 3, m\ge 3 are fixed integers and \beta is a fixed positive real power different from 1 satisfying the conventions 0^{\beta }:= 0 and 1^\beta:=1.
ISSN:1592-7415
2282-8214
DOI:10.23755/rm.v41i0.690