On functional inequalities associated with Drygas functional equation

Youssef Manar, Elhoucien Elqorachi
2014 Tbilisi Mathematical Journal  
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.
doi:10.2478/tmj-2014-0018 fatcat:tq3miihlsvbvxbsufaaxel2qze