Convergence theorems for monotone vector field inclusions and minimization problems in Hadamard spaces

Abstract

This article analyses two schemes: Mann-type and viscosity-type proximal point algorithms. Using these schemes, we establish Δ-convergence and strong convergence theorems for finding a common solution of monotone vector field inclusion problems, a minimization problem, and a common fixed point of multivalued demicontractive mappings in Hadamard spaces. We apply our results to find mean and median values of probabilities, minimize energy of measurable mappings, and solve a kinematic problem in robotic motion control. We also include a numerical example to show the applicability of the schemes. Our findings corroborate some recent findings.

Keywords

• fixed point
• monotone vector field
• proximal point algorithm
• resolvent operator
• tangent space
• 47h05
• 47j25
• 49j40
• 65k10
• 65k15