# On convexity of solutions of ordinary differential equations

## TL;DR

This paper proves that solutions of certain ordinary differential equations depend convexly on initial data within ordered finite-dimensional real vector spaces.

## Contribution

It establishes a new convexity property of solutions' dependence on initial conditions in the context of ordered vector spaces.

## Key findings

- Solutions exhibit convex dependence on initial data.
- The result applies to finite-dimensional real vector spaces with an order structure.
- Provides a theoretical foundation for convexity in ODE solutions.

## Abstract

We prove a result on the convex dependence of solutions of ordinary differential equations on an ordered finite-dimensional real vector space with respect to the initial data.