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 in:AIMS 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
Language:English
Published: AIMS Press 01.01.2024
Subjects:
fixed point problem
inertial extrapolation
strong convergence
variational inclusion
viscosity method
ISSN:2473-6988, 2473-6988
Online Access:Get full text
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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