Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces

Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces

© 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and l...

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Main Authors: Suantai S., Phuengrattana W.
Format: Journal
Published: 2017
Online Access:https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85014474299&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/40592
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Institution: Chiang Mai University
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spelling th-cmuir.6653943832-405922017-09-28T04:10:22Z Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces Suantai S. Phuengrattana W. © 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and lower semi-continuous functions. We obtain Δ -convergence and strong convergence of the proposed algorithm to a common element of the three sets in CAT(0) spaces. Furthermore, we apply our convergence results to obtain in a special space of CAT(0) spaces, so-called R-tree, under the gate condition. A numerical example to support our main results is also given. 2017-09-28T04:10:22Z 2017-09-28T04:10:22Z 2 Journal 16605446 2-s2.0-85014474299 10.1007/s00009-017-0876-z https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85014474299&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/40592
institution Chiang Mai University
building Chiang Mai University Library
country Thailand
collection CMU Intellectual Repository
description © 2017, Springer International Publishing. In this paper, we propose a new proximal point algorithm for finding a common element of the set of fixed points of nonexpansive single-valued mappings, the set of fixed points of nonexpansive multi-valued mappings, and the set of minimizers of convex and lower semi-continuous functions. We obtain Δ -convergence and strong convergence of the proposed algorithm to a common element of the three sets in CAT(0) spaces. Furthermore, we apply our convergence results to obtain in a special space of CAT(0) spaces, so-called R-tree, under the gate condition. A numerical example to support our main results is also given.
format Journal
author Suantai S.
Phuengrattana W.
spellingShingle Suantai S.
Phuengrattana W.
Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
author_facet Suantai S.
Phuengrattana W.
author_sort Suantai S.
title Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
title_short Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
title_full Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
title_fullStr Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
title_full_unstemmed Proximal Point Algorithms for a Hybrid Pair of Nonexpansive Single-Valued and Multi-Valued Mappings in Geodesic Metric Spaces
title_sort proximal point algorithms for a hybrid pair of nonexpansive single-valued and multi-valued mappings in geodesic metric spaces
publishDate 2017
url https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85014474299&origin=inward
http://cmuir.cmu.ac.th/jspui/handle/6653943832/40592
_version_ 1681421845971075072

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