## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 272867, 14 pages.

Dates
First available in Project Euclid: 26 March 2014

https://projecteuclid.org/euclid.aaa/1395858489

Digital Object Identifier
doi:10.1155/2014/272867

Mathematical Reviews number (MathSciNet)
MR3166587

Zentralblatt MATH identifier
07022063

#### Citation

Naraghirad, Eskandar; Wong, Ngai-Ching; Yao, Jen-Chih. Applications of Bregman-Opial Property to Bregman Nonspreading Mappings in Banach Spaces. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 272867, 14 pages. doi:10.1155/2014/272867. https://projecteuclid.org/euclid.aaa/1395858489

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