Generalized split null point of sum of monotone operators in Hilbert spaces

In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a sol...

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Autores principales:	Mebawondu Akindele A., Abass Hammed A., Oyewole Olalwale K., Aremu Kazeem O., Narain Ojen K.
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	generalized split monotone variational inclusion inertial iterative scheme firmly nonexpansive fixed point problem 47h06 47h09 47j05 47j25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/d01c36561d1f4b01a47954106af160f7
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id	oai:doaj.org-article:d01c36561d1f4b01a47954106af160f7
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spelling	oai:doaj.org-article:d01c36561d1f4b01a47954106af160f72021-12-05T14:10:45ZGeneralized split null point of sum of monotone operators in Hilbert spaces2391-466110.1515/dema-2021-0034https://doaj.org/article/d01c36561d1f4b01a47954106af160f72021-11-01T00:00:00Zhttps://doi.org/10.1515/dema-2021-0034https://doaj.org/toc/2391-4661In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.Mebawondu Akindele A.Abass Hammed A.Oyewole Olalwale K.Aremu Kazeem O.Narain Ojen K.De Gruyterarticlegeneralized split monotone variational inclusioninertial iterative schemefirmly nonexpansivefixed point problem47h0647h0947j0547j25MathematicsQA1-939ENDemonstratio Mathematica, Vol 54, Iss 1, Pp 359-376 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	generalized split monotone variational inclusion inertial iterative scheme firmly nonexpansive fixed point problem 47h06 47h09 47j05 47j25 Mathematics QA1-939
spellingShingle	generalized split monotone variational inclusion inertial iterative scheme firmly nonexpansive fixed point problem 47h06 47h09 47j05 47j25 Mathematics QA1-939 Mebawondu Akindele A. Abass Hammed A. Oyewole Olalwale K. Aremu Kazeem O. Narain Ojen K. Generalized split null point of sum of monotone operators in Hilbert spaces
description	In this paper, we introduce a new type of a generalized split monotone variational inclusion (GSMVI) problem in the framework of real Hilbert spaces. By incorporating an inertial extrapolation method and an Halpern iterative technique, we establish a strong convergence result for approximating a solution of GSMVI and fixed point problems of certain nonlinear mappings in the framework of real Hilbert spaces. Many existing results are derived as corollaries to our main result. Furthermore, we present a numerical example to support our main result and propose an open problem for interested researchers in this area. The result obtained in this paper improves and generalizes many existing results in the literature.
format	article
author	Mebawondu Akindele A. Abass Hammed A. Oyewole Olalwale K. Aremu Kazeem O. Narain Ojen K.
author_facet	Mebawondu Akindele A. Abass Hammed A. Oyewole Olalwale K. Aremu Kazeem O. Narain Ojen K.
author_sort	Mebawondu Akindele A.
title	Generalized split null point of sum of monotone operators in Hilbert spaces
title_short	Generalized split null point of sum of monotone operators in Hilbert spaces
title_full	Generalized split null point of sum of monotone operators in Hilbert spaces
title_fullStr	Generalized split null point of sum of monotone operators in Hilbert spaces
title_full_unstemmed	Generalized split null point of sum of monotone operators in Hilbert spaces
title_sort	generalized split null point of sum of monotone operators in hilbert spaces
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/d01c36561d1f4b01a47954106af160f7
work_keys_str_mv	AT mebawonduakindelea generalizedsplitnullpointofsumofmonotoneoperatorsinhilbertspaces AT abasshammeda generalizedsplitnullpointofsumofmonotoneoperatorsinhilbertspaces AT oyewoleolalwalek generalizedsplitnullpointofsumofmonotoneoperatorsinhilbertspaces AT aremukazeemo generalizedsplitnullpointofsumofmonotoneoperatorsinhilbertspaces AT narainojenk generalizedsplitnullpointofsumofmonotoneoperatorsinhilbertspaces
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Generalized split null point of sum of monotone operators in Hilbert spaces

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