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

Augustine L. Mahu; Benoît F. Sehba; Cecilia D. Williams

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

General Mathematics 2026-07-27 v1

Authors: Augustine L. Mahu , Benoît F. Sehba , Cecilia D. Williams

Abstract

We introduce a reflection-substitution technique for sine inequalities that yields, via H\"older'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.

Keywords

sine inequalities weighted products ratios Holder's inequality reflection-substitution dominance criteria

Cite

@article{arxiv.2607.26092,
  title  = {On some inequalities for weighted products and ratios of the sine function},
  author = {Augustine L. Mahu and Benoît F. Sehba and Cecilia D. Williams},
  journal= {arXiv preprint arXiv:2607.26092},
  year   = {2026}
}

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14 pages