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NEW ALGEBRAIC-TRIGONOMETRIC INEQUALITIES OF LAUB–ILANI TYPE

Part of: Inequalities

Published online by Cambridge University Press:  02 March 2017

AHMET YAŞAR ÖZBAN
AHMET YAŞAR ÖZBAN*
Affiliation:
Department of Mathematics, Atilim University, 06836 İncek, Ankara, Turkey email ahmet.ozban@atilim.edu.tr
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Abstract

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The Laub–Ilani inequality [‘A subtle inequality’, Amer. Math. Monthly97 (1990), 65–67] states that $x^{x}+y^{y}\geqslant x^{y}+y^{x}$ for nonnegative real numbers $x,y$. We introduce and prove new trigonometric and algebraic-trigonometric inequalities of Laub–Ilani type and propose some conjectural algebraic-trigonometric inequalities of similar forms.

Keywords

Laub–Ilani inequalityJordan’s inequalityconcave functiontrigonometric inequalityalgebraic-trigonometric inequality

MSC classification

Primary: 26D05: Inequalities for trigonometric functions and polynomials
Secondary: 26D07: Inequalities involving other types of functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 96 , Issue 1 , August 2017 , pp. 87 - 97
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

References

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