carpathian_2026_42_1_81-94Abstract.
Approximation of zeros of monotone operators can be applied to solve some nonlinear problems on Banach spaces such as function spaces. Similarly, a concept of monotone set-valued vector fields on geodesic spaces includes classes of convex minimisation problems and equilibrium problems. In this paper, we prove a zero point approximation theorem with a projection method for a monotone vector field on complete geodesic spaces. This method guarantees us to generate a sequence converging strongly to a zero point of a given set-valued vector field.
