Applications of Bregman-Opial property to Bregman nonspreading mappings in Banach spaces
نویسندگان
چکیده
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 an alike 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.
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