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...

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Bibliographic Details
Main Authors: Salisu Sani, Kumam Poom, Sriwongsa Songpon
Format: Article
Language:English
Published: De Gruyter 2023-04-01
Series:Analysis and Geometry in Metric Spaces
Subjects:
Online Access:https://doi.org/10.1515/agms-2022-0150
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