Hybrid algorithm for common solution of monotone inclusion problem and fixed point problem and applications to variational inequalities

被引：4
|
作者：
Zhang, Jingling [1 ]
Jiang, Nan [1 ]
机构：
[1] Tianjin Univ, Dept Math, Tianjin 300350, Peoples R China
来源：
SPRINGERPLUS | 2016年 / 5卷
基金：
中国国家自然科学基金;
关键词：
Quasi-nonexpansive mappings; Inverse-strongly monotone mapping; Maximal monotone operator; Fixed point; CONVERGENCE THEOREMS; EQUILIBRIUM PROBLEMS; NONEXPANSIVE-MAPPINGS; ITERATIVE ALGORITHM; ACCRETIVE OPERATOR; ZERO-POINT; APPROXIMATION; ELEMENTS;
D O I：
10.1186/s40064-016-2389-9
中图分类号：
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
The aim of this paper is to investigate hybrid algorithm for a common zero point of the sum of two monotone operators which is also a fixed point of a family of countable quasi-nonexpansive mappings. We point out two incorrect proof in paper (Hecai in Fixed Point Theory Appl 2013:11, 2013). Further, we modify and generalize the results of Hecai's paper, in which only a quasi-nonexpansive mapping was considered. In addition, two family of countable quasi-nonexpansive mappings with uniform closeness examples are provided to demonstrate our results. Finally, the results are applied to variational inequalities.
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页数：13
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