# Nonsymmetric extension of the Green-Osher inequality

## TL;DR

This paper extends the Green-Osher inequality to a nonsymmetric setting for smooth, convex planar bodies, establishing conditions for equality and broadening its applicability.

## Contribution

It introduces a nonsymmetric extension of the Green-Osher inequality with necessary and sufficient conditions for equality in the planar convex case.

## Key findings

- Extended Green-Osher inequality to nonsymmetric convex bodies
- Established necessary and sufficient conditions for equality
- Applied to smooth, planar strictly convex bodies

## Abstract

In this paper we obtain the extended Green-Osher inequality when two smooth, planar strictly convex bodies are at a dilation position and show the necessary and sufficient condition for the case of equality.