Abstract
In this work, we present the viscosity method for the implicit double midpoint rule for finding the fixed points of nonexpansive mappings in real Hilbert spaces. The strong convergence theorem of this method is proved under some specific assumption imposed on the control parameters. Also, we present some numerical results which are presented to illustrate the proposed method and convergence results. Moreover, we provide the applications to the variational inequality problems, constrained convex minimization problems, nonlinear evolution equations, and Fredholm integral equations.
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Acknowledgements
The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under grant no. MRG6180283 for financial support during the preparation of this manuscript.
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Communicated by Carlos Conca.
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Dhakal, S., Sintunavarat, W. The viscosity method for the implicit double midpoint rule with numerical results and its applications. Comp. Appl. Math. 38, 40 (2019). https://doi.org/10.1007/s40314-019-0811-y
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DOI: https://doi.org/10.1007/s40314-019-0811-y