arXiv subjects

Augustine L. Mahu

Publications and source records attributed to Augustine L. Mahu.

2 recordsLinked to original sources

arXiv2026

On some inequalities for weighted products and ratios of the sine function

We introduce a reflection-substitution technique for sine inequalities that yields, via Hölder's inequality and its reverse, $2^{n-1}$ distinct upper bounds for products and lower bounds for ratios of weighted sines. The comparison between bounds reduces to simple sign conditions on linear combinations of the variables. We fully classify the two- and three-dimensional cases, providing explicit dominance criteria with detailed examples for each signature.

math.GM↗

arXiv2026

Weighted Product Inequalities for the Sine Function: A Gamma-Function Approach and Sharp Comparisons

Using the log-convexity of the Gamma function and Euler's reflection formula, we give a new proof of a classical weighted sine product inequality. Two different parameter choices yield two competing upper bounds for the same product. We determine precisely, via algebraic criteria, when one bound is sharper than the other. Explicit results are given for the general $n$-angle case, the $2n$-angle case, and for two and three angles. Several sharp corollaries are derived, including $\sin(πx)\leq \sin(2πx(1-x))$.

math.GM↗