ADDITIVE - QUARTIC FUNCTIONAL EQUATIONS ARE STABLE IN RANDOM NORMED SPACE: A FIXED POINT METHOD

M. Arunkumara,*, S. Murthyb, S. Hema Lathac, M. Arulselvand

ADDITIVE - QUARTIC FUNCTIONAL EQUATIONS ARE STABLE IN RANDOM NORMED SPACE: A FIXED POINT METHOD

Authors :

M. Arunkumar^a,*, S. Murthy^b, S. Hema Latha^c, M. Arulselvan^d

Author Address :

^aDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.
^bDepartment of Mathematics, Government Arts College for Men, Krishnagiri-635 001, Tamil Nadu, India.
^cDepartment of Mathematics,Annai Veilankanni’s College of Arts and Science, Chennai - 600 015, TamilNadu, India.
^dSRGDS Matriculation Hr. Sec. School,Tiruvannamalai - 606 604, TamilNadu, India

Abstract :

Applying fixed point method, the generalized Ulam - Hyers stability of additive-quartic functional equation and 2- variable additive - quartic functional equation of the forms
\begin{align*}
f(2x + y) + f(2x -y) &= 4\left[f(x+y)+f(x-y)\right] + 12[f(x)+f(-x)] \\
& \qquad\qquad\qquad - 3[f(y)+f(-y)] - 2[f(x)-f(-x)]
\end{align*}
and
\begin{align*}
&g(2u+v,2y+z) + g(2u - v,2y - z)\\
&\qquad \qquad=4\left[g(u + v,y + z) + g(u - v,y - z) \right]+ 12[g(u,y) + g(- u,- y)]\\
& \qquad\qquad\qquad\qquad\qquad\qquad\qquad- 3[g(v,z) + g(- v,-z)] - 2[g(u,y) - g(-u,-y)]
\end{align*}
in Random normed spaces is studied.

Keywords :

Additive-quartic mixed functional equations, generalized Ulam - Hyers stability, Random Normed space, fixed point.

DOI :

Article Info :

Received : April 19, 2015; Accepted : May 05, 2015.