Asymptotic behavior of support points for planar curves

TL;DR

This paper establishes a universal inequality governing the asymptotic behavior of support points on planar curves, with implications for tangent points and classical analytic theorems, and presents open questions for further research.

Contribution

It introduces a new universal inequality for support points on planar curves and explores its implications for tangent points and mean value points in analysis.

Findings

Derived a universal inequality for support points

Connected support points to tangent points and mean value points

Formulated open questions for future research

Abstract

In this paper we prove a universal inequality describing the asymptotic behavior of support points for planar continuous curves. As corollaries we get an analogous result for tangent points of differentiable planar curves and some (partially known) assertions on the asymptotic of the mean value points for various classical analytic theorems. Some open questions are formulated.