Viscosity-type inertial iterative methods for variational inclusion and fixed point problems

Mohammad Dilshad; Fahad Maqbul Alamrani; Ahmed Alamer; Esmail Alshaban; Maryam G. Alshehri; Mohammad Dilshad; Fahad Maqbul Alamrani; Ahmed Alamer; Esmail Alshaban; Maryam G. Alshehri

doi:10.3934/math.2024903

AIMS Mathematics

2024, Volume 9, Issue 7: 18553-18573. doi: 10.3934/math.2024903

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Viscosity-type inertial iterative methods for variational inclusion and fixed point problems

Department of Mathematics, Faculty of Science, University of Tabuk, Tabuk-71491, Saudi Arabia

Received: 12 March 2024 Revised: 07 May 2024 Accepted: 28 May 2024 Published: 03 June 2024
MSC : 47H05, 47H06, 49J53

In this paper, we have introduced some viscosity-type inertial iterative methods for solving fixed point and variational inclusion problems in Hilbert spaces. Our methods calculated the viscosity approximation, fixed point iteration, and inertial extrapolation jointly in the starting of every iteration. Assuming some suitable assumptions, we demonstrated the strong convergence theorems without computing the resolvent of the associated monotone operators. We used some numerical examples to illustrate the efficiency of our iterative approaches and compared them with the related work.
- viscosity method,
- inertial extrapolation,
- fixed point problem,
- variational inclusion,
- strong convergence
Citation: Mohammad Dilshad, Fahad Maqbul Alamrani, Ahmed Alamer, Esmail Alshaban, Maryam G. Alshehri. Viscosity-type inertial iterative methods for variational inclusion and fixed point problems[J]. AIMS Mathematics, 2024, 9(7): 18553-18573. doi: 10.3934/math.2024903

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Abstract

In this paper, we have introduced some viscosity-type inertial iterative methods for solving fixed point and variational inclusion problems in Hilbert spaces. Our methods calculated the viscosity approximation, fixed point iteration, and inertial extrapolation jointly in the starting of every iteration. Assuming some suitable assumptions, we demonstrated the strong convergence theorems without computing the resolvent of the associated monotone operators. We used some numerical examples to illustrate the efficiency of our iterative approaches and compared them with the related work.

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