Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces

© 2019, Wilmington Scientific Publisher. All rights reserved. In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the pa...

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Main Authors:	Prasit Cholamjiak, Suthep Suantai, Pongsakorn Sunthrayuth
Format:	Journal
Published:	2020
Subjects:	Mathematics
Online Access:	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85074669201&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67896
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Institution:	Chiang Mai University

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spelling	th-cmuir.6653943832-678962020-04-02T15:10:29Z Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth Mathematics © 2019, Wilmington Scientific Publisher. All rights reserved. In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the parameters in the framework of Hilbert spaces. As applications, we apply our main result to the split feasibility problem and the LASSO problem. We also give some numerical examples to support our main result. The results presented in this paper extend and improve the corresponding results in the literature. 2020-04-02T15:10:29Z 2020-04-02T15:10:29Z 2019-12-01 Journal 21585644 2156907X 2-s2.0-85074669201 10.11948/20180191 https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85074669201&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67896
institution	Chiang Mai University
building	Chiang Mai University Library
country	Thailand
collection	CMU Intellectual Repository
topic	Mathematics
spellingShingle	Mathematics Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
description	© 2019, Wilmington Scientific Publisher. All rights reserved. In this paper, we study a general viscosity explicit rule for approximating the solutions of the variational inclusion problem for the sum of two monotone operators. We then prove its strong convergence under some new conditions on the parameters in the framework of Hilbert spaces. As applications, we apply our main result to the split feasibility problem and the LASSO problem. We also give some numerical examples to support our main result. The results presented in this paper extend and improve the corresponding results in the literature.
format	Journal
author	Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth
author_facet	Prasit Cholamjiak Suthep Suantai Pongsakorn Sunthrayuth
author_sort	Prasit Cholamjiak
title	Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
title_short	Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
title_full	Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
title_fullStr	Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
title_full_unstemmed	Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
title_sort	strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces
publishDate	2020
url	https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85074669201&origin=inward http://cmuir.cmu.ac.th/jspui/handle/6653943832/67896
_version_	1681426719865569280

Strong convergence of a general viscosity explicit rule for the sum of two monotone operators in hilbert spaces

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