# Strong geodesic convex functions of order m

## TL;DR

This paper introduces the concept of strong geodesic convex functions of order m on Riemannian manifolds, providing characterizations and linking them to variational inequalities and multiobjective optimization.

## Contribution

It establishes the properties of strong geodesic convex functions of order m and connects these to variational inequalities and optimization solutions.

## Key findings

- Characterization of strong geodesic convex functions of order m
- Relation between variational inequality solutions and strict minimizers
- Extension of convexity concepts to Riemannian manifolds

## Abstract

Strong geodesic convex function and strong monotone vector field of order $m$ on Riemannian manifolds have been established. A characterization of strong geodesic convex function of order $m$ for the continuously differentiable functions has been discussed. The relation between the solution of a new variational inequality problem and the strict minimizers of order $m$ for a multiobjective programming problem has also been established.