Hybrid iterative algorithm for finite families of countable Bregman quasi-Lipschitz mappings with applications in Banach spaces

详细信息    查看全文

• 作者：Minjiang Chen ; Jianzhi Bi ; Yongfu Su
• 关键词：Bregman distance ; Bregman quasi ; Lipschitz mapping ; generalized projection ; hybrid algorithm ; Bregman asymptotically quasi ; nonexpansive mappings ; finite families ; equilibrium problem
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,605 KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

The purpose of this paper is to introduce and consider a new hybrid shrinking projection method for finding a common element of the set EP of solutions of a generalized equilibrium problem, the common fixed point set F of finite uniformly closed families of countable Bregman quasi-Lipschitz mappings in reflexive Banach spaces. It is proved that under appropriate conditions, the sequence generated by the hybrid shrinking projection method converges strongly to some point in \(\mathit{EP} \cap F\). Relative examples are given. Strong convergence theorems are proved. The application for Bregman asymptotically quasi-nonexpansive mappings is also given. The main innovative points in this paper are as follows: (1) the notion of the uniformly closed family of countable Bregman quasi-Lipschitz mappings is presented and the useful conclusions are given; (2) the relative examples of the uniformly closed family of countable Bregman quasi-Lipschitz mappings are given in classical Banach spaces \(l^{2}\) and \(L^{2}\); (3) the application for Bregman asymptotically quasi-nonexpansive mappings is also given; (4) because the main theorems do not need the boundedness of the domain of mappings, so a corresponding technique for the proof is given. This new results improve and extend the previously known ones in the literature.