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^{1*}, E. Sathya^{2}, S. Karthikeyan^{3}, G. Ganapathy^{4}, T. Namachivayam^{5}

**Author Address : **

^{1,2,5}Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.

^{3}Department of Mathematics, R.M.K. Engineering College, Kavarapettai - 601 206, TamilNadu, India.

^{4}Department 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

egin{align*}

&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

end{align*}

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 -<

**DOI : **

**Article Info : **

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