Orthogonal stability of the new generalized quadratic functional equation

K. Ravi; S. Suresh

doi:10.26637/mjm304/013

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
$\begin{align*} &f(n x+y)+f(n x-y)=n[f(x+y)+f(x-y)]\\&+2 n(n-1) f(x)-2(n-1) f(y), \end{align*}$
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, Orthogonally quadratic functional equation, Orthogonality space, Quadratic mapping

Mathematics Subject Classification:

39B55, 39B52, 39B82, 46H25

Authors Imprint References Funding Related Articles Downloads

K. Ravi Department of Mathematics, Sacred Hart College, Tiruppatur, Tamil Nadu, India.
S. Suresh Research Scholar,Bharathiar University, Coimbatore-642002, Tamil Nadu, India.

Pages: 554-562
Date Published: 01-10-2015
Vol. 3 No. 04 (2015): Malaya Journal of Matematik (MJM)

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