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

Applications of Bregman-Opial property to Bregman nonspreading mappings in Banach spaces. (English) Zbl 1428.47028

Abstr. Appl. Anal. 2014, Article ID 272867, 14 p. (2014).
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.

Cited in 6 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.

Keywords:

Bregman-Opial property; Mann iteration; Ishikawa iteration; weak convergence; strong convergence; Bregman nonspreading mappings
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\textit{E. Naraghirad} et al., Abstr. Appl. Anal. 2014, Article ID 272867, 14 p. (2014; Zbl 1428.47028)
Full Text: DOI

References:

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