REFINEMENTS AND REVERSES OF F ́EJER’S INEQUALITIES FOR CONVEX FUNCTIONS ON LINEAR SPACES

Abstract

. Let f be an convex function on the convex set C in a linear space and x; y 2 C; with x 6 = y: If p : [0 ; 1] ! [0 ; 1 ) is Lebesgue integrable and symmetric, namely p (1 t = p ( t for all 2 [0 ; 1] ; then where r (cid:6) f ( ) are the G(cid:226)teaux lateral derivatives. Some applications for norms and semi-inner products are also provided.