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

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 mu...

Full description

Saved in:
Bibliographic Details
Published in:Analysis and Geometry in Metric Spaces 2023-04, Vol.11 (1), p.1029-1039
Main Authors: Salisu, Sani, Kumam, Poom, Sriwongsa, Songpon
Format: Article
Language:English
Subjects:
47H05
47J25
49J40
65K10
65K15
Algorithms
Convergence
Fields (mathematics)
fixed point
Inclusions
Kinematics
monotone vector field
Motion control
Optimization
proximal point algorithm
resolvent operator
Robot control
tangent space
Theorems
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:2299-3274
2299-3274
DOI:10.1515/agms-2022-0150