多值Bregman全拟渐近非扩张映像的强收敛性

张石生, 王林, 赵云河, 王刚

数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 213-226.

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数学学报 ›› 2015, Vol. 58 ›› Issue (2) : 213-226. DOI: 10.12386/A2015sxxb0022
论文

多值Bregman全拟渐近非扩张映像的强收敛性

    张石生, 王林, 赵云河, 王刚
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Strong Convergence of Multi-Valued Bregman Totally Quasi-Asymptotically Nonexpansive Mappings

    Shi Sheng ZHANG, Lin WANG, Yun He ZHAO, Gang WANG
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摘要

建立了一种算法, 用以寻求自反 Banach 空间中多值 Bregman全拟渐近非扩张映像的有限族的公共不动点,改进和推广了以前的结果(算法是基于与一凸函数有关的 Bregman 距离). 最后,把所得的结果应用于平衡系统问题, 自反 Banach空间中极大单调映像的零点问题.

Abstract

We propose an algorithms for finding a common fixed point of a finite family of multi-valued Bregman total quasi-φ-asymptotically nonexpansive mappings in reflexive Banach spaces. The results presented in the paper improve and extend the corresponding new results announced by many authors. The algorithms are based on the Bregman distance related to a well-chosen convex function. As applications, we apply our results to a system of equilibrium problems and zero point problem of maximal monotone mappings in reflexive Banach spaces.

关键词

非扩张映像 / 全凸函数 / Bregman 投影

Key words

nonexpansive mapping / totally convex function / Bregman projection

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张石生, 王林, 赵云河, 王刚. 多值Bregman全拟渐近非扩张映像的强收敛性. 数学学报, 2015, 58(2): 213-226 https://doi.org/10.12386/A2015sxxb0022
Shi Sheng ZHANG, Lin WANG, Yun He ZHAO, Gang WANG. Strong Convergence of Multi-Valued Bregman Totally Quasi-Asymptotically Nonexpansive Mappings. Acta Mathematica Sinica, Chinese Series, 2015, 58(2): 213-226 https://doi.org/10.12386/A2015sxxb0022

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基金

国家自然科学基金资助项目(11361070)

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