# Variational Inequalities on Geodesic Spaces

## TL;DR

This paper introduces a new variational inequality problem in $CAT(0)$ spaces involving nonself multivalued nonexpansive mappings, expanding the theoretical framework of variational inequalities in metric spaces.

## Contribution

It presents a novel variational inequality problem tailored for $CAT(0)$ spaces with nonself multivalued nonexpansive mappings, extending existing VIP theories.

## Key findings

- Defines a new VIP in $CAT(0)$ spaces
- Establishes foundational properties of the new VIP
- Lays groundwork for future solution methods

## Abstract

In this paper, we introduce a new variational inequality problem(VIP) associated with nonself multivalued nonexpansive mappings in $CAT(0)$ spaces.