ORTHOGONAL STABILITY OF THE NEW GENERALIZED QUADRATIC FUNCTIONAL EQUATION

K. Ravia,* and S.Sureshb

ORTHOGONAL STABILITY OF THE NEW GENERALIZED QUADRATIC FUNCTIONAL EQUATION

Authors :

K. Ravi^a,* and S.Suresh^b

Author Address :

^aDepartment of Mathematics, Sacred Hart College, Tiruppatur, India.
^bResearch Scholar, Bharathiar University, Coimbatore-642046, Tamil Nadu, India.

*Coressponding author.

Abstract :

In this paper, the authors investigate the Hyers - Ulam - Rassias stability and J. M. Rassias mixed type product- sum of powers of norms stability of a orthogonally generalized quadratic functional equation of the form
\begin{equation*}
f\left(nx+y\right)+f\left(nx-y\right)=n[f\left(x+y\right)+f\left(x-y\right)]+2n(n-1)f(x)-2(n-1)f(y).
\end{equation*}
Where $f:A \rightarrow B$ be a mapping from a orthogonality normed space $A$ into a Banach Space $B$, $\perp$ is orthogonality in the sense of Ratz with $x \perp y$ for all $x, y \in A$.

Keywords :

Hyers - Ulam - Rassias stability, J. M. Rassias mixed type product - sum of powers of norms stability, Example, Orthogonally quadratic functional equation, Orthogonality space, Quadratic mapping.

DOI :

Article Info :

Received : October 10, 2015; Accepted : January 23, 2016.