Multistep hybrid viscosity method for split monotone variational inclusion and fixed point problems in Hilbert spaces

In this paper, we present a multi-step hybrid iterative method. It is proven that under appropriate assumptions, the proposed iterative method converges strongly to a common element of fixed point of a finite family of nonexpansive mappings, the solution set of split monotone variational inclusion p...

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Bibliographic Details
Published inAIMS mathematics Vol. 5; no. 6; pp. 5969 - 5992
Main Authors Abubakar, Jamilu, Kumam, Poom, Deepho, Jitsupa
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2020
Subjects
fixed point problem
hilbert spaces
split monotone variational inclusion
triple hierarchical variational inequality problem
variational inequality problem
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Summary:In this paper, we present a multi-step hybrid iterative method. It is proven that under appropriate assumptions, the proposed iterative method converges strongly to a common element of fixed point of a finite family of nonexpansive mappings, the solution set of split monotone variational inclusion problem and the solution set of triple hierarchical variational inequality problem (THVI) in real Hilbert spaces. In addition, we give a numerical example of a triple hierarchical system derived from our generalization.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2020382