On Gauss-Polya's Inequality

Let g;h :âa;ba!R be nonnegative nondecreasing functions such that g and h have a continuous ¢rst derivative and gOaUahOaU;gObUahObU. Let paOp1;p2U be ap air of positive real numbersp1;p2 such that p1a p2a 1. a) If f :âa;ba!R be a nonnegative nondecreasing function, then for r;s < 1 M âra p O b