Ulam-Hyers stability of Euler-Lagrange additive functional equation in  intuitionistic fuzzy Banach spaces: Direct and fixed point methods

M. Arunkumar1*, E. Sathya2, S. Ramamoorthi3, P. Agilan4

doi:10.26637/MJM0601/0031

Ulam-Hyers stability of Euler-Lagrange additive functional equation in intuitionistic fuzzy Banach spaces: Direct and fixed point methods

Authors :

M. Arunkumar^1*, E. Sathya², S. Ramamoorthi³, P. Agilan⁴

Author Address :

^1,2Department of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
³Department of Mathematics, Arunai Engineering College, Tiruvannamalai, TamilNadu, India - 606 603.
⁴Department of Mathematics, Jeppiaar Institute of Technology, Sriperumbudur, Chennai - 631 604, Tamil Nadu, India.

*Corresponding author.

Abstract :

In this paper, authors verify the generalized Ulam - Hyers stability of the following
Euler - Lagrange additive functional equation
egin{align*}
rfleft(sleft(x-y ight) ight) + sfleft(rleft(y-x ight) ight)
+ left(r+s ight)fleft(rx+sy ight)
= left(r+s ight)left(rfleft(x ight) + sfleft(y ight) ight)
%% y = x
%% left(r + s ight)fleft(left( r + s ight)x} ight) = left(r + s ight)^2 fleft( x ight)
end{align*}
in Intuitionistic Fuzzy Banach Spaces using direct and fixed point methods.

Keywords :

Additive functional equations, Euler - Lagrange functional equations, generalized Ulam - Hyers stability, intuitionistic fuzzy Banach Space, fixed point.

DOI :

10.26637/MJM0601/0031

Article Info :

Received : November 04, 2017; Accepted : December 28, 2017.