Inequalities for indefinite forms
Authors offer for indefinite forms \((x_1^p-x_2^p-...-x_n^p)^{1/p}\) a comparison result (they increase in \(p\)) and generalizations of \textit{R. Bellman}'s [Am. Math. Mon. 63, 108-109 (1956; Zbl 0070.27805)] and \textit{T. Popoviciu}'s [Gaz. Mat. Fiz., Bucur., Ser. A. 11(64), 451-461 (1959; Zbl 0101.04101)] inequalities. They note that Popoviciu's inequality has been misquoted by \textit{D. S. Mitrinović} [``Analytic inequalities'' (1970; Zbl 0199.38101), p. 58] and by \textit{M. Bjelica} [Math., Rev. Anal. Numér. Théor. Approximation, Anal. Numér. Théor. Approximation 19, No. 2, 105-109 (1990, Zbl 0733.26011)]. But the inequality which Bjelica did prove also follows from the authors' results.
scientific article; zbMATH DE number 1005705
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