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Viscosity approximations by generalized contractions for resolvents of accretive operators in Banach spaces

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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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Authors and Affiliations

  1. Department of Applied Mathematics, Babeş-Bolyai University, 400084, Cluj-Napoca, Romania

    Adrian Petruşel

  2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, 804

    Jen-Chih Yao

Authors
  1. Adrian Petruşel
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  2. Jen-Chih Yao
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Correspondence to Jen-Chih Yao.

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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

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