Ulam - Hyers stability of a 2- variable AC - mixed type functional equation in quasi - beta normed spaces: direct and fixed point methods

John  M. Rassiasa, M. Arunkumarb,*, S. Ramamoorthic, and S. Hemalathad

Ulam - Hyers stability of a 2- variable AC - mixed type functional equation in quasi - beta normed spaces: direct and fixed point methods

Authors :

John M. Rassias^a, M. Arunkumar^b,*, S. Ramamoorthi^c, and S. Hemalatha^d

Author Address :

^aPedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, Athens 15342, Greece.

^bDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.

^cDepartment of Mathematics, Arunai Engineering College, Tiruvannamalai - 606 604, TamilNadu, India.

^dDepartment of Mathematics, Annai Veilankanni’s College of Arts and Science, Saidapet, Chennai - 600 015.

*Corresponding author.

Abstract :

In this paper, we obtain the generalized Ulam - Hyers stability of a 2 - variable AC - mixed type functional equation
egin{align*}
f(2x+y, 2z+w) - f(2x-y, 2z-w)= 4[f(x+y, z+w) - f(x-y, z-w)]- 6f(y, w)
end{align*}
in Quasi - Beta normed space using direct and fixed point methods.

Keywords :

Additive functional equations, cubic functional equations, Mixed type AC functional equations, generalized Ulam - Hyers stability, fixed point.

DOI :

Article Info :

Received : December 09, 2013; Accepted : January 05, 2014.