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
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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References
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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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