Tbilisi Mathematical Journal

On functional inequalities associated with Drygas functional equation

Youssef Manar and Elhoucien Elqorachi

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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, $(E, \lt\cdot, \cdot\gt)$ is an inner product space, and the norm is derived from the inner product in the usual way.

Article information

Source
Tbilisi Math. J., Volume 7, Issue 2 (2014), 73-78.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528768977

Digital Object Identifier
doi:10.2478/tmj-2014-0018

Mathematical Reviews number (MathSciNet)
MR3313057

Zentralblatt MATH identifier
1307.39013

Subjects
Primary: 39B62: Functional inequalities, including subadditivity, convexity, etc. [See also 26A51, 26B25, 26Dxx]
Secondary: 39B52: Equations for functions with more general domains and/or ranges

Keywords
group Cauchy equation Quadratic equation Drygas equation

Citation

Manar, Youssef; Elqorachi, Elhoucien. On functional inequalities associated with Drygas functional equation. Tbilisi Math. J. 7 (2014), no. 2, 73--78. doi:10.2478/tmj-2014-0018. https://projecteuclid.org/euclid.tbilisi/1528768977


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