Lagrange’s Quadratic Functional Equation Connected with Homomorphisms and Derivations on Lie $C^*$-algebras: Direct and Fixed Point Methods

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Authors :

John M. Rassiasa, M. Arunkumarb and S. Karthikeyanc,*

Author Address :

aPedagogical Department E.E., Section of Mathematics and Informatics, National and Capodistrian University of Athens, 4, 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.

*Corresponding author.

Abstract :

In this paper, we obtain the general solution in vector space and the generalized Ulam-Hyers stability of Lagrange’s quadratic functional equation of the form
\begin{align*}
\left(\sum\limits^{n}_{i=1}f(x_i)\right)\left(\sum\limits^{n}_{i=1}f(y_i)\right) = f\left(\sum\limits^{n}_{i=1} x_i y_i\right)+
\sum_{1\le i<j\le n}f\left(x_i y_j-x_j y_i\right)
\end{align*}
where $n$ is a positive integer on Lie $C^*$-algebras using direct and fixed point methods. An application of this functional equation is also studied.

Keywords :

Quadratic functional equation, Generalized Ulam-Hyers stability, Lie -algebra, Fixed point method.

DOI :

Article Info :

Received : April 15, 2015; Accepted : May 23, 2015.