In this paper, we investigate the right and left Bregman weakly relatively nonexpansive operators in reflexive Banach spaces. We first introduce the notions of convex hull demi-closedness principle, strictly strongly convex hull demi-closedness principle, strongly demi-closedness principle, and composition demi-closedness principle of a family of nonlinear mappings using another new notions of convex asymptotic fixed points, and composition asymptotic fixed points for such mappings in a Banach space E. We analyze, in particular, compositions and convex combinations of Bregman weakly relatively nonexpansive operators, and prove the convergence of the Mann iterative method for operators of these types. Finally, we use our results to approximate common zeros of maximal monotone mappings and solutions to convex feasibility problems. To support our results, we include nontrivial examples in the paper. Therefore, our results improve and generalize many known results in the current literature.

中文翻译：

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自反Banach空间中Bregman弱相对非扩张算子的组成和凸组合

在本文中，我们研究了自反Banach空间中右Bregman和左Bregman弱相对非扩张算子。首先，我们使用另一种新的凸渐近不动点概念，介绍了非线性映射族的凸壳半封闭原理，严格强凸壳半封闭原理，强半封闭原理和构图半封闭原理， Banach空间E中此类映射的结构和组成渐近不动点。我们特别分析了Bregman弱相对不扩张算子的组成和凸组合，并证明了Mann迭代方法对于此类算子的收敛性。最后，我们使用我们的结果来近似最大单调映射的公共零点和凸可行性问题的解。为了支持我们的结果，我们在论文中包含了一些简单的例子。因此，我们的结果改进并概括了当前文献中的许多已知结果。