A generalization of the Hölder inequality through dynamic programming approach (Q1115981)

This paper generalizes the Hölder inequality to one with ordered constraint and with lower bound through dynamic programming (DP) approach. \textit{G. S. Mudholker, M. Freimer} and \textit{P. Subbaiah} [J. Math. Anal. Appl. 102, 435-441 (1984; Zbl 0563.26013)] extended the Hölder inequality to one with the ordered constraint by Lagrange's multiplier method, and \textit{M. Freimer} and \textit{G. S. Mudholker} [Proc. Sympos. Inequalities in statistics and probability, IMS Lecture-Notes- Monograph, Ser. 5, 59-67 (1984)] generalized it by use of Kuhn-Tucker condition in mathematical programming. Later, the authors generalized the Hölder inequality by applying a majorization theorem. In this paper, the authors extend further the generalized Hölder inequality to one with the ordered constraint and with a lower parametric bound by solving three pairs of main (maximum) and inverse (minimum) DP problems without appealing to majorization theorem of any kind.