Abstract.
We complement, extend, and sharpen some known inequalities for sine sums. Our main result is the following refinement of the classical Fejér-Jackson inequality: For all integers n ⩾ 2 and real numbers x ∈ (0,π) we have
with the best possible constant factor α = 1. This improves an inequality due to Turán.
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Received February 12, 2002 Published online April 4, 2003
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Alzer, H., Koumandos, S. Inequalities of Fejér-Jackson Type. Monatsh. Math. 139, 89–103 (2003). https://doi.org/10.1007/s00605-002-0523-y
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DOI: https://doi.org/10.1007/s00605-002-0523-y