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

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Authors :

M. Arunkumar1*, E. Sathya2, S. Karthikeyan3, G. Ganapathy4, T. Namachivayam5

Author Address :

1,2,5Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
3Department of Mathematics, R.M.K. Engineering College, Kavarapettai - 601 206, TamilNadu, India.
4Department of Mathematics, R.M.D. Engineering College,Kavaraipettai - 601 206, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, authors proved the generalized Ulam - Hyers stability of system of additive functional equations
&fleft(sum_{a =1}^{n}~a~x_a ight)
=sum_{a =1}^{n}left(a~f(x_a) ight);qquad ngeq1
&gleft(sum_{a =1}^{n}~2a~y_{2a} ight)
=sum_{a =1}^{n}left(2a~g(y_{2a}) ight);qquad ngeq1
&hleft(sum_{a =1}^{n}~(2a-1)~z_{2a-1} ight)
= sum_{a =1}^{n}left((2a-1)~h(z_{2a-1}) ight);qquad ngeq1
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.

Keywords :

Additive functional equations, Generalized Ulam - Hyers stability, Banach spaces, 2-Banach space, Quasi 2 - Banach space, Quasi - Beta - 2- Banach space, Fuzzy Quasi -<



Article Info :

Received : December 01, 2017; Accepted : December 27, 2017.



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