On functional inequalities associated with Drygas functional equationsY. Manar, El. Elqorachi
In the paper, the equivalence of the functional inequality
|2f(x)+f(y)+f(-y)-f(x-y)|≤|f(x+y)| (x,y ϵ G )
and the Drygas functional equation
f(x+y)+f(x-y)=2f(x)+f(y)+f(-y) (x,y ϵ 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.
Tbilisi Mathematical Journal, Vol. 7(2) (2014), pp. 73-78 |