(untitled) (Letters in Nonlinear Analysis and its Applications, 2025)
In this paper, we propose a notion of monotone set-valued vector fields on geodesic spaces with curvature bounded above, and define a resolvent operator of a monotone vector field. Particularly, we investigate a relation between zero points of a monotone vector field and fixed points of its resolvent operator, and asymptotic behaviours of resolvent operators. Finally, we consider two examples of monotone vector fields corresponding to the subdifferential of convex functions. To constitute the examples, we consider resolvent operators of convex functions and equilibrium problems, respectively.