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- 2018
渐近半伪压缩映射合成隐迭代序列的强收敛性
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Abstract:
参照Banach压缩映照原理，合理引进了一涉及有限族渐近半伪压缩映射的具误差的合成隐迭代序列.在一致凸Banach空间中，研究该合成隐迭代序列的强收敛性，得到了具误差的合成隐迭代序列强收敛于有限族渐近半伪压缩的公共不动点的充要条件.
In this paper, a new composite implicit iterative scheme with errors for a finite family of asymptotically hemi-pseudocontractive mappings is reasonably introduced in view of the Banach's contraction principle. The purpose of this paper is to study strong convergence of the composite implicit iterative scheme for a family of asymptotically hemi-pseudocontractive mappings in the uniformly convex Banach space, and some necessary and sufficient conditions for the strong convergence of this iterative scheme to a common fixed point of these mappings are obtained
| [1] | GUO W, GUO Q. Convergence Theorems of Fixed Points for Asymptotically Hemi-Pseudocontractive Mappings[J]. Appl Math Comput, 2009, 215(1): 16-21. |
| [2] | ZHOU Y Y, CHANG S S. Convergence of Implicit Iteration Process for A Finite Family of Asymptotically Nonexpansive Mappings in Banach Spaces[J]. Numer Funct Anal Optimiz, 2002, 23(7-8): 911-921. DOI:10.1081/NFA-120016276 |
| [3] | GU F. Approximate Fixed Point Sequence for A Finite Family of Asymptotically Pseudocontractive Mappings[J]. Comput Math Appl, 2007, 53(12): 1792-1799. DOI:10.1016/j.camwa.2006.12.017 |
| [4] | LIU Y Q, GUO W P. A Sufficient and Neccessary Condition for the Strong Convergence of Asymptotically Hemi-Pseudontractive Mapping[J]. J of Math (PRC), 2015, 35(4): 747-753. |
| [5] | 唐玉超, 刘理蔚. 赋范线性空间中渐近伪压缩映象不动点迭代逼近的充分必要条件[J]. 南昌大学学报(理学版), 2010, 34(3): 210-213. |
| [6] | 刘涌泉, 郭伟平. 混合型渐近非扩张映射合成隐迭代序列的收敛性定理[J]. 数学物理学报, 2015, 35(2): 422-440. |
| [7] | 杨理平, 胡刚. 具随机性误差隐迭代程序的收敛性[J]. 数学学报, 2008, 51(1): 11-22. |
| [8] | XU H K, ORI R G. An Implicit Iteration Process for Nonexpansive Mappings[J]. Numer Funct Anal Optimiz, 2001, 22(5-6): 767-773. DOI:10.1081/NFA-100105317 |
| [9] | BARBU V. Nonlinear Semigroups and Differential Equations in Banach Spaces[M]. Leyden: Noordhoff International Publishing, 1976. |
| [10] | GOEBEL K, KIRK W A. A Fixed Point Theorem for Asymptotically Nonexpansive Mappings[J]. Proc Amer Math Soc, 1972, 35(1): 171-174. DOI:10.1090/S0002-9939-1972-0298500-3 |
| [11] | 刘文军, 孟京华, 邓中书. 渐近拟非扩张型映象的修正的Ishikawa Riech-Takahashi迭代序列的强收敛性[J]. 江西师范大学学报(自然科学版), 2011, 35(3): 297-301. DOI:10.3969/j.issn.1000-5862.2011.03.019 |
| [12] | 饶若峰. 渐近非扩张映像具误差的合成隐迭代序列的弱收敛和强收敛定理[J]. 数学年刊A辑(中文版), 2008, 29(4): 461-470. |
| [13] | KAN X Z, GUO W P. Composite Implicit Iteration Process for a Lipschitzian Pseudocontractive Mapping[J]. J of Math (PRC), 2014, 34(1): 1-6. |
| [14] | 陈清明, 欧增奇. 集值非扩张映象的不动点及带误差的Ishikawa迭代序列的收敛性[J]. 西南大学学报(自然科学版), 2015, 37(10): 62-66. |
| [15] | LIU Q. Iteration Sequences for Asymptotically Quasi-Nonexpansive Mapping with an Error Member of Uniform Convex Banach Space[J]. J Math Anal App, 2002, 266(2): 468-471. DOI:10.1006/jmaa.2001.7629 |
| [16] | TAN K K, XU H K. Approximating Fixed Points of Nonexpansive Mappings By the Ishikawa Iteration Process[J]. J Math Anal Appl, 1993, 178(2): 301-308. DOI:10.1006/jmaa.1993.1309 |
