Journal of Applied Mathematics
- J. Appl. Math.
- Volume 2014, Special Issue (2014), Article ID 573075, 9 pages.
Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces
We study Mann type iterative algorithms for finding fixed points of Bregman relatively nonexpansive mappings in Banach spaces. By exhibiting an example, we first show that the class of Bregman relatively nonexpansive mappings embraces properly the class of Bregman strongly nonexpansive mappings which was investigated by Martín-Márques et al. (2013). We then prove weak convergence theorems for the sequences produced by the methods. Some application of our results to the problem of finding a zero of a maximal monotone operator in a Banach space is presented. Our results improve and generalize many known results in the current literature.
J. Appl. Math., Volume 2014, Special Issue (2014), Article ID 573075, 9 pages.
First available in Project Euclid: 1 October 2014
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Pang, Chin-Tzong; Naraghirad, Eskandar; Wen, Ching-Feng. Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces. J. Appl. Math. 2014, Special Issue (2014), Article ID 573075, 9 pages. doi:10.1155/2014/573075. https://projecteuclid.org/euclid.jam/1412177570