One step proximal point schemes for monotone vector field inclusion problems

In this paper, we propose one step convex combination of proximal point algorithms for
countable collection of monotone vector fields in CAT(0) spaces. We establish delta-convergence and
strong convergence theorems for approximating a common solution of a countable family of monotone
vector field inclusion problems. Furthermore, we apply our methods to solve a family of minimization
problems, compute Frech´et mean and geometric median in CAT(0) spaces, and solve a kinematic
problem in robotic motion control. Finally, we give a numerical example to show the efficiency and
robustness of the proposed scheme in comparison to a known scheme in the literature.