Resolvents of equilibrium problems in a complete geodesic space with negative curvature

TL;DR

This paper introduces a resolvent for equilibrium problems in negatively curved geodesic spaces, establishing its well-definedness and fundamental properties in such geometric contexts.

Contribution

It defines a new resolvent for equilibrium problems in complete geodesic spaces with negative curvature, proving its key properties and domain characteristics.

Findings

The resolvent is well-defined as a single-valued mapping.

The resolvent's fundamental properties are established.

The domain of the resolvent covers the entire space.

Abstract

In this paper, we propose a resolvent of an equilibrium problem in a geodesic space with negative curvature having the convex hull finite property. We prove its well-definedness as a single-valued mapping whose domain is whole space, and study the fundamental properties.