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

Eskandar Naraghirad, Ngai-Ching Wong and Jen-Chih Yao

Abstract and Applied Analysis, 2014, vol. 2014, 1-14

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:272867

DOI: 10.1155/2014/272867

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