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TWO NEW GENERALISED HYPERSTABILITY RESULTS FOR THE DRYGAS FUNCTIONAL EQUATION
Published online by Cambridge University Press: 09 January 2017
Abstract
Let $X$ be a nonempty subset of a normed space such that
$0\notin X$ and
$X$ is symmetric with respect to
$0$ and let
$Y$ be a Banach space. We study the generalised hyperstability of the Drygas functional equation
$$\begin{eqnarray}f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{eqnarray}$$
$f$ maps
$X$ into
$Y$ and
$x,y\in X$ with
$x+y,x-y\in X$. Our first main result improves the results of Piszczek and Szczawińska [‘Hyperstability of the Drygas functional equation’, J. Funct. Space Appl.2013 (2013), Article ID 912718, 4 pages]. Hyperstability results for the inhomogeneous Drygas functional equation can be derived from our results.
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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.
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