5 citations · 9 across the 6 of their papers we have counts for
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Inequalities for trigonometric sums
Horst Alzer, Man Kam Kwong
We present several new inequalities for trigonometric sums. Among others, we show that the inequality $$ \sum_{k=1}^n (n-k+1)(n-k+2)k\sin(kx) > \frac{2}{9} \sin(x) \bigl( 1+2\cos(x…
Sharp Bounds for the Arc Lemniscate Sine Function
Horst Alzer, Man Kam Kwong
The arc lemniscate sine function is given by $$ \mbox{arcsl}(x)=\int_0^x \frac{1}{\sqrt{1-t^4}}dt. $$ In 2017, Mahmoud and Agarwal presented bounds for $\mbox{arcsl}$ in terms of t…
Technical Details of the Proof of the Sine Inequality \\[1.2ex] {\normalsize
Man Kam Kwong
In a recent study, H. Alzer and the author showed that the sine polynomial is nonnegative for $ x\i…
A Refinement of Vietoris Inequality for Cosine Polynomials
Horst Alzer, Man Kam Kwong
The classical Vietoris cosine inequality is refined by establishing a positive polynomial lower bound.
A Hardy-Littlewood Integral Inequality on Finite Intervals with a Concave Weight
Horst Alzer, Man Kam Kwong
A Hardy-Littlewood integral inequality on finite intervals with a concave weight is established. Given a function f on an interval [a,b], it is shown that the square of the weighte…
Nonnegative Trigonometric Polynomials and Sturms Theorem
Man Kam Kwong
In an earlier article [3], we presented an algorithm that can be used to rigorously check whether a specific cosine or sine polynomial is nonnegative in a given interval or not. Th…