Abstract
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
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This research is partially supported by a grant from the National Science Council
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Petruşel, A., Yao, JC. Viscosity approximations by generalized contractions for resolvents of accretive operators in Banach spaces. Acta. Math. Sin.-English Ser. 25, 553–564 (2009). https://doi.org/10.1007/s10114-009-7362-x
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DOI: https://doi.org/10.1007/s10114-009-7362-x
Keywords
- viscosity approximation method
- accretive operator
- generalized contraction
- resolvent
- proximal point algorithm