Abstract
It is shown by an example that the best (greatest possible) value of the constant K in the Goldberg-Straus combinatorial inequality for normed vectors over the complex field is less than the known best value of K for vectors over the real field. For n = 2, the exact best value of K is here determined in the complex case.
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References
Moshe Goldberg and E. G. Straus, Combinatorial Inequalities, Matrix Norms, and Generalized Numerical Radii, in E. F. Beckenbach (ed.), General Inequalities2, Proceedings of the Second International Conference on General Inequalities, Mathematical Institute Oberwolfach, 1978, ISNM 47, Birkhäuser Verlag, Basel, Stuttgart, 1980, pp. 37–46. (Additional references are given here.)
Ray Redheffer and Carey Smith, On a surprising inequality of Goldberg and Straus, to appear in Amer. Math. Monthly.
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Redheffer, R.M., Smith, C. (1980). The Case n = 2 of the Goldberg-Straus Inequality. In: Beckenbach, E.F. (eds) General Inequalities 2. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 47. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6324-7_5
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DOI: https://doi.org/10.1007/978-3-0348-6324-7_5
Publisher Name: Birkhäuser, Basel
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