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Stability of system of additive functional equations in various Banach spaces: Classical Hyers methods

Stability of system of additive functional equations in various Banach spaces: Classical Hyers methods

Authors :
M. Arunkumar
E. Sathya
S. Karthikeyan
G. Ganapathy
T. Namachivayam
M. Arunkumar
E. Sathya
S. Karthikeyan
G. Ganapathy
T. Namachivayam
Source :
Malaya Journal of Matematik; Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM); 91-112; 2321-5666; 2319-3786
Publication Year :
2018

Abstract

In this paper, authors proved the generalized Ulam - Hyers stability of system of additive functional equations$$\begin{aligned}& f\left(\sum_{a=1}^n a x_a\right)=\sum_{a=1}^n\left(a f\left(x_a\right)\right) ; \quad n \geq 1 \\& g\left(\sum_{a=1}^n 2 a y_{2 a}\right)=\sum_{a=1}^n\left(2 a g\left(y_{2 a}\right)\right) ; \quad n \geq 1 \\& h\left(\sum_{a=1}^n(2 a-1) z_{2 a-1}\right)=\sum_{a=1}^n\left((2 a-1) h\left(z_{2 a-1}\right)\right) ; \quad n \geq 1\end{aligned}$$where $n$ is a positive integer, which is originating from sum of first $n$, natural numbers, even natural numbers and odd natural numbers, respectively in various Banach spaces.

Details

Database :
OAIster
Journal :
Malaya Journal of Matematik; Vol. 6 No. 01 (2018): Malaya Journal of Matematik (MJM); 91-112; 2321-5666; 2319-3786
Notes :
application/pdf, English
Publication Type :
Electronic Resource
Accession number :
edsoai.on1391126444
Document Type :
Electronic Resource