ON THE DIFFERENCE OPERATOR OF GRADIENT OF C1,1 -FUNCTIONS ON HILBERT SPACES

Abstract

Let f be a C1,1
-function on a nonempty open subset of the Hilbert space H.
Denote by M the Lipschitz constant of the gradient f . With an added conditio
of f, author prove the following inequalities
        
2 2 1 M
f (x) f (y) f(x) f(y) f(y),x y x y .
2M 2