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, $(E, \lt\cdot, \cdot\gt)$ is an inner product space, and the norm is derived from the inner product in the usual way.
Citation
Youssef Manar. Elhoucien Elqorachi. "On functional inequalities associated with Drygas functional equation." Tbilisi Math. J. 7 (2) 73 - 78, 2014. https://doi.org/10.2478/tmj-2014-0018
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