A generalization of the Hölder inequality through dynamic programming approach
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.
scientific article; zbMATH DE number 4087945
scientific article