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2014 Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces
Eskandar Naraghirad, Ngai-Ching Wong, Jen-Chih Yao
Abstr. Appl. Anal. 2014(SI57): 1-14 (2014). DOI: 10.1155/2014/272867


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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Eskandar Naraghirad. Ngai-Ching Wong. Jen-Chih Yao. "Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces." Abstr. Appl. Anal. 2014 (SI57) 1 - 14, 2014.


Published: 2014
First available in Project Euclid: 26 March 2014

zbMATH: 07022063
MathSciNet: MR3166587
Digital Object Identifier: 10.1155/2014/272867

Rights: Copyright © 2014 Hindawi


Vol.2014 • No. SI57 • 2014
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