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Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball

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  • Yasunori Kimura

Abstract

We propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball.

Suggested Citation

  • Yasunori Kimura, 2010. "Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    • Handle: RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:582475
    DOI: 10.1155/2010/582475
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    References listed on IDEAS

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    1. Takanori Ibaraki & Yasunori Kimura & Wataru Takahashi, 2003. "Convergence theorems for generalized projections and maximal monotone operators in Banach spaces," Abstract and Applied Analysis, Hindawi, vol. 2003, pages 1-9, January.
    2. Takanori Ibaraki & Yasunori Kimura & Wataru Takahashi, 2003. "Convergence theorems for generalized projections and maximal monotone operators in Banach spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2003(10), pages 621-629.
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    Cited by:

    1. Yasunori Kimura, 2016. "A shrinking projection method for nonexpansive mappings with nonsummable errors in a Hadamard space," Annals of Operations Research, Springer, vol. 243(1), pages 89-94, August.

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