18 citations · 42 across the 13 of their papers we have counts for
14 papers
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 Numerical Procedure for Proving Specific Strict One-Variable Inequalities in Specific Finite Intervals
Man Kam Kwong
A numerical procedure and its MAPLE implementation capable of rigorously, albeit in a brute-force manner, proving specific strict one-variable inequalities in specific finite inter…
On a Sine Polynomial of Turan
Horst Alzer, Man Kam Kwong
In 1935, P. Turán proved that We present various related inequalities. Among others, w…
A New Family of Nonnegative Sine Polynomials
Man Kam Kwong
We present a new family of sine polynomials that are nonnegative for all in . We also characterize all nonnegative sine polynomials of degree 3 and all nonnegative cosin…
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…
Improved Vietoris Sine Inequalities for Non-Monotone, Non-Decaying Coefficients
Man Kam Kwong
Recently the author established an improvement of the classical Vietoris sine inequality to include sine polynomials with non-monotone coefficients. In this paper two further impro…
On Hopital-style rules for monotonicity and oscillation
Man Kam Kwong
We point out the connection of the so-called Hôpital-style rules for monotonicity and oscillation to some well-known properties of concave/convex functions. From this standpoint, w…
Periodic Solutions of 2D Isothermal Euler-Poisson Equations with Possible Applications to Spiral and Disk-like Galaxies
Man Kam Kwong, Manwai Yuen
Compressible Euler-Poisson equations are the standard self-gravitating models for stellar dynamics in classical astrophysics. In this article, we construct periodic solutions to th…
Sturm Theorem and a Refinement of Vietoris Inequality for Cosine Polynomials
Horst Alzer, Man Kam Kwong
In a recent work, the authors established a refinement of the well-known 1958 result of Vietoris on nonnegative cosine polynomials. In four places of the proof, use was made of the…
Nonnegative Trigonometric Polynomials, Sturms Theorem, and Symbolic Computation
Man Kam Kwong
In this paper, we explain a procedure based on a classical result of Sturm that can be used to determine rigorously whether a given trigonometric polynomial is nonnegative in a cer…