On converses of Hölder and Beckenbach inequalities
Recently, \textit{Y.-D. Zhuang} [J. Math. Anal. Appl. 161, No. 2, 566-575 (1991; Zbl 0752.26005)] obtained an inverse of the Hölder inequality. Using this result, it is also possible to obtain an inverse of the Beckenbach inequality where the ``best constant'' appears to be the same as in the corresponding inverse Hölder inequality. In this paper, the authors recall another inverse of the Hölder inequality due to \textit{J. B. Diaz}, \textit{A. J. Goldman} and \textit{F. T. Metcalf} [J. Res. Natl. Bur. Stand. Sect. B 68, 147-149 (1964; Zbl 0125.03001)] and derive another inverse of the Beckenbach inequality where the best constant remains also unchanged.
scientific article; zbMATH DE number 861851