Quartic Functional Equation  Involving Sum of Functions of Consecutive Variables  is Stable in Felbin’s Type Cone Normed Spaces

S. Murthy a , M. Maria Susai Manuel b , M. Arunkumar c and G. Ganapathy d,∗

Quartic Functional Equation Involving Sum of Functions of Consecutive Variables is Stable in Felbin’s Type Cone Normed Spaces

Authors :

S. Murthy ^a, M. Maria Susai Manuel ^b , M. Arunkumar ^c and G. Ganapathy ^d,∗

Author Address :

^a Department of Mathematics, Government Arts College for Men, Krishnagiri-635 001, Tamil Nadu, India.
^b,d Department of Mathematics, R.M.D. Engineering College, Kavaraipettai - 601 206, Tamil Nadu, India
^cDepartment of Mathematics, Government Arts College, Tiruvannamalai - 606 603, TamilNadu, India.

*Corresponding author

Abstract :

In the notion of Ulam problem, several stability results invented for different type of functional equation in many spaces. Further, the researchers used the concept of alternative fixed point theorem in stability of functional equation. In that motivation, we introduce the generalized Ulam - Hyers stability of a quartic functional equation involving sum of functions of consecutive variables
\begin{align*}
\sum\limits_{i=1}^nf\left(\sum\limits_{j=1}^ix_j\right) &= \sum\limits_{i=1}^n\sum\limits_{1\leq j <k<l <m\leq i}^{}f(x_j+x_k+x_l+x_m)
-\sum\limits_{i=1}^n(i-4) \sum\limits_{1\leq j < k<l \leq i}^{} f(x_j+x_k+x_l)\notag\\
&~~~ + \sum\limits_{i=1}^n \left(\frac{(i-3)(i-4)}{2}\right) \sum\limits_{1\leq j <k\leq i}^{} f(x_j+x_k)
-\frac{1}{16}\sum\limits_{i=1}^n\left(\frac{(i-4)(i-3)(i-2)}{6}\right)\sum\limits_{ j= 1}^{i}f(2x_j)
\end{align*}
with $n>5$ in Felbins type cone normed space and its solution in real vector space is presented.

Keywords :

Quartic functional equations, Generalized Ulam - Hyers stability, Felbin’s type Fuzzy Cone normed space, Fixed point.

DOI :

Article Info :

Received : June 10, 2016; Accepted : December 17, 2016.