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Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces

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  • Eskandar Naraghirad
  • Ngai-Ching Wong
  • Jen-Chih Yao

Abstract

The Opial property of Hilbert spaces and some other special Banach spaces is a powerful tool in establishing fixed point theorems for nonexpansive and, more generally, nonspreading mappings. Unfortunately, not every Banach space shares the Opial property. However, every Banach space has a similar Bregman-Opial property for Bregman distances. In this paper, using Bregman distances, we introduce the classes of Bregman nonspreading mappings and investigate the Mann and Ishikawa iterations for these mappings. We establish weak and strong convergence theorems for Bregman nonspreading mappings.

Suggested Citation

  • Eskandar Naraghirad & Ngai-Ching Wong & Jen-Chih Yao, 2014. "Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-14, January.
    • Handle: RePEc:hin:jnlaaa:272867
    DOI: 10.1155/2014/272867
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