TWO NEW GENERALISED HYPERSTABILITY RESULTS FOR THE DRYGAS FUNCTIONAL EQUATION
2017 ◽
Vol 95
(2)
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pp. 269-280
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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 $$\begin{eqnarray}f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{eqnarray}$$ where $f$ 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.
1980 ◽
Vol 32
(2)
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pp. 421-430
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1969 ◽
Vol 10
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pp. 73-76
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2013 ◽
Vol 89
(1)
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pp. 33-40
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2015 ◽
Vol 93
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pp. 272-282
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2011 ◽
Vol 9
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pp. 205-215
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1988 ◽
Vol 110
(3-4)
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pp. 199-225
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