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Strong convergence of an iterative sequence for maximal monotone operators in a Banach space

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  • Fumiaki Kohsaka
  • Wataru Takahashi

Abstract

We first introduce a modified proximal point algorithm for maximal monotone operators in a Banach space. Next, we obtain a strong convergence theorem for resolvents of maximal monotone operators in a Banach space which generalizes the previous result by Kamimura and Takahashi in a Hilbert space. Using this result, we deal with the convex minimization problem and the variational inequality problem in a Banach space.

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  • Fumiaki Kohsaka & Wataru Takahashi, 2004. "Strong convergence of an iterative sequence for maximal monotone operators in a Banach space," Abstract and Applied Analysis, Hindawi, vol. 2004, pages 1-11, January.
    • Handle: RePEc:hin:jnlaaa:240462
    DOI: 10.1155/S1085337504309036
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    Cited by:

    1. Ali Abkar & Elahe Shahrosvand & Azizollah Azizi, 2017. "The Split Common Fixed Point Problem for a Family of Multivalued Quasinonexpansive Mappings and Totally Asymptotically Strictly Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 5(1), pages 1-18, February.

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