An extension of a Bourgain–Lindenstrauss–Milman inequality

An Operator Extension of Bohr's inequality

an operator extension of bohr's inequality

An extension of Maclaurins inequality

Let G be a graph of order n and clique number !: For every x = (x1; : : : ; xn) 2 Rn and 1 s !; set fs (G;x) = X fxi1 : : : xis : fi1; : : : ; isg is an s-clique of Gg ; and let s (G;x) = fs (G;x) ! s 1 : We show that if x 0; then 1 (G;x) 1=2 2 (G;x) 1=! ! (G;x) : This extends the inequality of Maclaurin (G = Kn) and generalizes the inequality of Motzkin and Straus. In addition, if x > 0; for e...

An extension of McDiarmid's inequality

We derive an extension of McDiarmid’s inequality for functions f with bounded differences on a high probability set Y (instead of almost surely). The behavior of f outside Y may be arbitrary. The proof is short and elementary, and relies on an extension argument similar to Kirszbraun’s theorem [4].

An Extension of Peleg’s Inequality

In this note we prove an extension of a remarkable result due to B. Peleg. Peleg’s result concerning with the simultaneous validity of a set of inequalities for families of functions defined on a finite product of standard simplices in finite dimensional spaces. The main result we prove here provides an extension of that result to the case of functions defined on a rather general product of sim...