Existence Results for Particular Instances of the Vector Quasi-Equilibrium Problem on Hadamard Manifolds

TL;DR

This paper establishes existence results for vector quasi-variational inequalities and related fixed point problems on Hadamard manifolds, expanding the theoretical understanding of these problems in non-Euclidean spaces.

Contribution

It provides new existence theorems for vector quasi-variational inequalities on Hadamard manifolds, a setting less explored in prior research.

Findings

Existence results for vector optimization problems on Hadamard manifolds

Validity of solutions for generalized vector quasi-variational inequalities

Application to fixed point problems in non-Euclidean geometry

Abstract

We show the validity of select existence results for a vector optimization problem, and a variational inequality. More generally, we consider generalized vector quasi-variational inequalities, as well as, fixed point problems on genuine Hadamard manifolds.