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

Jamilu Abubakar; Poom Kumam; Jitsupa Deepho; Jamilu Abubakar; Poom Kumam; Jitsupa Deepho

doi:10.3934/math.2020382

AIMS Mathematics

2020, Volume 5, Issue 6: 5969-5992. doi: 10.3934/math.2020382

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Research article

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

1.
KMUTTFixed Point Research Laboratory, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT) 126 Pracha Uthit Rd., Bang Mod, Thrung Khru, Bangkok 10140, Thailand
2.
Department of Mathematics, Usmanu Danfodiyo University, P.M.B. 2346, Sokoto, Nigeria
3.
Faculty of Science, Energy and Environment, King Mongkut’s University of Technology North Bangkok (KMUTNB) 19 Moo 11, Tambon Nonglalok, Amphur Bankhai, Rayong 21120, Thailand

Received: 27 April 2020 Accepted: 08 July 2020 Published: 22 July 2020
MSC : 47H05, 47H10, 47J22, 49J40

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.
Citation: Jamilu Abubakar, Poom Kumam, Jitsupa Deepho. Multistep hybrid viscosity method for split monotone variational inclusion and fixed point problems in Hilbert spaces[J]. AIMS Mathematics, 2020, 5(6): 5969-5992. doi: 10.3934/math.2020382

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Abstract

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.

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