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Some Trigonometric Inequalities

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Recent Advances in Geometric Inequalities

Part of the book series: Mathematics and Its Applications ((MAEE,volume 28))

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Abstract

In the book [1] one finds that almost all triangles inequalities are symmetric in form when expressed in terms of the sides a, b, c or the angles A, B, C of a given triangle. No doubt that also assymmetric triangle inequalities play a very important role in geometric inequalities. It should be noted that many of these inequalities are still valid for real numbers A, B, C which satisfy the condition

$$ A + B + C = p\pi , $$

where p is a natural number (which has to be odd in some cases). This also applies to the inequality of M. S. Klamkin [2] which can be specialized in many ways to obtain numerous well known inequalities.

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Authors and Affiliations

  1. University of Belgrade, Yugoslavia

    D. S. Mitrinović

  2. University of Zagreb, Yugoslavia

    J. E. Pečarić & V. Volenec

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  1. D. S. Mitrinović
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  2. J. E. Pečarić
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  3. V. Volenec
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© 1989 Springer Science+Business Media Dordrecht

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Mitrinović, D.S., Pečarić, J.E., Volenec, V. (1989). Some Trigonometric Inequalities. In: Recent Advances in Geometric Inequalities. Mathematics and Its Applications, vol 28. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7842-4_6

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  • DOI: https://doi.org/10.1007/978-94-015-7842-4_6

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-8442-2

  • Online ISBN: 978-94-015-7842-4

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