Open Access
Translator Disclaimer
2014 On functional inequalities associated with Drygas functional equation
Youssef Manar, Elhoucien Elqorachi
Author Affiliations +
Tbilisi Math. J. 7(2): 73-78 (2014). DOI: 10.2478/tmj-2014-0018

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

Download 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

Information

Received: 29 September 2014; Accepted: 17 November 2014; Published: 2014
First available in Project Euclid: 12 June 2018

zbMATH: 1307.39013
MathSciNet: MR3313057
Digital Object Identifier: 10.2478/tmj-2014-0018

Subjects:
Primary: ‎39B62
Secondary: 39B52‎

Rights: Copyright © 2014 Tbilisi Centre for Mathematical Sciences

JOURNAL ARTICLE
6 PAGES


SHARE
Vol.7 • No. 2 • 2014
Back to Top