Beckenbach inequality and its variants
One of the most interesting generalizations of the Hölder inequality was proved as Theorem 1 given on page 24 of \textit{E. F. Beckenbach} [J. Math. Anal. Appl. 15, 21-29 (1966; Zbl 0141.241)]. This generalization is now known as the Beckenbach inequality [see the author, J. Math. Anal. Appl. 71, 423-430 (1979; Zbl 0425.26009); ibid. 72, 355-361 (1979; Zbl 0425.26008); ibid. 95, 564-574 (1983; Zbl 0524.26012); and the author and \textit{S. Iwamoto}, ibid. 118, 279-286 (1986; Zbl 0593.26011)]. In this paper, we proved the Beckenbach inequality and its continuous counterpart by a direct use of the usual Hölder inequality.
generalizations of the Hölder inequality
scientific article; zbMATH DE number 4046052