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Hong-Kun Xu, Najla Altwaijry, Imtithal Alzughaibi, Souhail Chebbi, The viscosity approximation method for accretive operators in Banach spaces

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DOI: 10.23952/jnva.6.2022.1.03

Volume 6, Issue 1, 1 February 2022, Pages 37-50

 

Abstract. We extend the viscosity approximation method (VAM) to accretive operators (via their resolvents) in a uniformly convex and/or uniformly G√Ęteau differentiable Banach space X to find a zero of an m-accretive operator and of the sum of two m-accretive operators. In all cases, we prove the strong convergence of our VAM algorithms and the limit of the iterates is identified as the unique sunny nonexpansive retraction onto to the zero set of the operator.

 

How to Cite this Article:
Hong-Kun Xu, Najla Altwaijry, Imtithal Alzughaibi, Souhail Chebbi, The viscosity approximation method for accretive operators in Banach spaces, J. Nonlinear Var. Anal. 6 (2022), 37-50.