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arXiv · 1405.7942

On functional inequalities associated with Drygas functional equation

Manar Youssef·Elqorachi Elhoucien
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Abstract

In the paper, the equivalence of the functional inequality $$\|2f(x)+f(y)+f(-y)-f(x-y)\|\leq\|f(x+y)\|\;\;\;(x,y\in{G})$$ and the Drygas functional equation $$f(x+y)+f(x-y)=2f(x)+f(y)+f(-y)\;\;\;(x,y\in{G})$$ is proved for functions $f:G\rightarrow E$ where $(G, +)$ is an abelian group, $(E, <\cdot, \cdot>)$ is an inner product space, and the norm is derived from the inner product in the usual way.

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Manar Youssef, Elqorachi Elhoucien. 2014-05-21. On functional inequalities associated with Drygas functional equation. https://arxiv.org/abs/1405.7942

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