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

Journal article

Authors/Editors

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Publication Details

Author list: Salisu, Sani; Kumam, Poom; Sriwongsa, Songpon;

Publisher: De Gruyter

Publication year: 2023

Volume number: 11

Issue number: 1

ISSN: 2299-3274

eISSN: 2299-3274

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85158000544&doi=10.1515%2fagms-2022-0150&partnerID=40&md5=84fa88aface62a5017d4e892511c302c

Languages: English-Great Britain (EN-GB)

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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. © 2023 the author(s), published by De Gruyter.

Keywords

monotone vector field, resolvent operator, tangent space