New Steffensen-type inequalities are obtained by combining generalized Taylor expansions, Rabier and Pečarić extensions of Steffensen’s inequality Faà di Bruno’s formula for higher order derivatives the composition.

Our aim is to give a version of the Moser-Trudinger inequality in setting complex geometry. As very particular case, our result already gives new for functions Sobolev space $W^{1,2}$ domain $R^2$. We also deduce necessary condition Monge-Ampere equation given measure on compact Kahler manifold admit Holder continuous solution.

 We consider generalized semi-infinite programming problems in which the index set of the inequality constraints depends on the decision vector and all emerging functions are assumed to be convex. Considering a lower level constraint qualification, we derive a formula for estimating the subdifferential of the value function. Finally, we establish the Fritz-John necessary optimality con...

A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric inequalities of plane convex geometry: The Blaschke-Santalo inequality and the affine isoperimetric inequality of affine differential geometry.