1. TWO NEW GENERALISED HYPERSTABILITY RESULTS FOR THE DRYGAS FUNCTIONAL EQUATION.
- Author
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AIEMSOMBOON, LADDAWAN and SINTUNAVARAT, WUTIPHOL
- Subjects
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FUNCTIONAL equations , *SET theory , *NORMED rings , *BANACH spaces , *FIXED point theory , *INTEGERS , *ADDITIVE functions - 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]
- Published
- 2017
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