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TWO NEW GENERALISED HYPERSTABILITY RESULTS FOR THE DRYGAS FUNCTIONAL EQUATION.
- Source :
-
Bulletin of the Australian Mathematical Society . Apr2017, Vol. 95 Issue 2, p269-280. 12p. - Publication Year :
- 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 $$\begin{eqnarray}f(x+y)+f(x-y)=2f(x)+f(y)+f(-y),\end{eqnarray}$$ 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. [ABSTRACT FROM PUBLISHER]
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 95
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 121496036
- Full Text :
- https://doi.org/10.1017/S000497271600126X