Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces
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 B...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/272867 |
| Summary: | 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. |
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| ISSN: | 1085-3375 1687-0409 |