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

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 iterat...

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Bibliographic Details
Published inAIMS mathematics Vol. 9; no. 7; pp. 18553 - 18573
Main Authors Dilshad, Mohammad, Alamrani, Fahad Maqbul, Alamer, Ahmed, Alshaban, Esmail, Alshehri, Maryam G.
Format Journal Article
LanguageEnglish
Published AIMS Press 01.01.2024
Subjects
fixed point problem
inertial extrapolation
strong convergence
variational inclusion
viscosity method
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Summary: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.
ISSN:2473-6988
2473-6988
DOI:10.3934/math.2024903