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Tbilisi Mathematical Journal

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On functional inequalities associated with Drygas functional equation

Youssef Manar
  • Corresponding author
  • Superior School of Technology, University Ibn Zohr, Guelmim, Morocco
  • Faculty of Sciences, Department of Mathematics, Agadir, Morocco
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Elhoucien Elqorachi
Published Online: 2014-12-30 | DOI: https://doi.org/10.2478/tmj-2014-0018


In the paper, the equivalence of the functional inequality ∥2f(x) + f(y) + f(-y) - f(x - y)∥ ≤ ∥f(x + y)∥ (x,y ∈ G) and the Drygas functional equation f(x + y) + f(x - y) = 2f(x) + f(y) + f(-y) (x,y ∈ G) is proved for functions f : G → E where (G, +) is an abelian group, (E,<.,.>) is an inner product space, and the norm is derived from the inner product in the usual way.

Keywords: group; Cauchy equation; Quadratic equation; Drygas equation


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Published Online: 2014-12-30

Citation Information: Tbilisi Mathematical Journal, Volume 7, Issue 2, ISSN (Online) 1512-0139, DOI: https://doi.org/10.2478/tmj-2014-0018.

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