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A complementary triangle inequality in Hilbert and Banach spaces. (English) Zbl 0173.41202


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[1] Herbert S. Wilf, Some applications of the inequality of arithmetic and geometric means to polynomial equations, Proc. Amer. Math. Soc. 14 (1963), 263 – 265. · Zbl 0192.16501
[2] J. B. Diaz and F. T. Metcalf, Complementary inequalities. I. Inequalities complementary to Cauchy’s inequality for sums of real numbers, J. Math. Anal. Appl. 9 (1964), 59 – 74. · Zbl 0135.34702 · doi:10.1016/0022-247X(64)90006-X
[3] J. B. Diaz and F. T. Metcalf, Complementary inequalities. II. Inequalities complementary to the Buniakowsky-Schwarz inequality for integrals, J. Math. Anal. Appl. 9 (1964), 278 – 293. · Zbl 0135.34702 · doi:10.1016/0022-247X(64)90006-X
[4] G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, Cambridge University Press, New York, 1959. · Zbl 0634.26008
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