Some theorems on reverse inequalities (Q1084527)

This paper treats the reversion of inequalities like as arithmetic mean- geometric mean, Cauchy, Hölder, Mitrinović, Szegö, Iwamoto, and others. In particular it is shown that Cauchy and Aczél, Hölder and Popoviciu, and Minkowski and Lorentz inequalities are dual in the reverse sense. These inequalities and their reversed forms in both discrete and continuous cases are established through dynamic programming approach. Each inequality on one or two recursive function(s) with strict increasingness is reversible. The reverse inequality states a dual relation on its or their reverse function(s). Here recursive function with strict increasingness is a sequentially parametric composition of a class of strictly increasing continuous functions. Reversion is also a sequentially parametric extension of inversion.