A note on the Neuman-S\'andor Mean
Tie-Hong Zhao, Yu-Ming Chu, Bao-Yu Liu
TL;DR
This paper establishes optimal bounds for the Neuman-Sándor mean using various combinations of classical means, enhancing understanding of its mathematical properties and relationships.
Contribution
It provides the best possible bounds for the Neuman-Sándor mean in terms of specific mean combinations, which was not previously known.
Findings
Derived tight bounds for the Neuman-Sándor mean.
Connected the Neuman-Sándor mean with harmonic, quadratic, and contra-harmonic means.
Enhanced the theoretical understanding of mean inequalities.
Abstract
In this article, we present the best possible upper and lower bounds for the Neuman-S\'andor mean in terms of the geometric combinations of harmonic and quadratic means, geometric and quadratic means, harmonic and contra-harmonic means, and geometric and contra-harmonic means.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Inequalities and Applications · Functional Equations Stability Results · Iterative Methods for Nonlinear Equations