共查询到19条相似文献,搜索用时 124 毫秒
1.
刘涌泉 《数学的实践与认识》2021,(2):259-267
引入了两个单值非扩张映射与两有限族多值非扩张映射新的混合迭代,在Banach空间中,研究了两个单值非扩张映射与两有限族多值非扩张映射在新迭代下关于公共不动点的收敛性,改进和推广了已有文献相关的结果. 相似文献
2.
3.
4.
蔡钢 《数学物理学报(A辑)》2015,(3):487-502
该文首先研究吸引非扩张映射的性质,然后在一致光滑Banach空间里,用这些性质研究两个非扩张映射的不动点问题的粘性迭代算法.作为应用,在Banach空间或Hilbert空间里,得到了关于变分不等式问题,不动点问题和均衡问题的强收敛定理.所得结果提高和推广了许多最近的相关结果. 相似文献
5.
研究了两个多值非扩张映射的公共不动点的迭代逼近问题.利用Hausdoff度量,引入了一类新的Ischikawa型迭代,在一致凸的Banach空间里,证明了在某些条件下,此迭代序列强收敛到多值非扩张映射的公共不动点.改进和推广了文献的相关结果. 相似文献
6.
利用CQ方法修正了渐近非扩张映射的Ishikawa迭代,并证明修正迭代过程强收敛,此结果推广并改进了一些相关结论. 相似文献
7.
《数学的实践与认识》2019,(23)
在Hilbert空间框架下,给出并研究了非扩张映射的一类广义的隐粘性迭代方法,在合适的条件下,证明了迭代程序所生成的序列强收敛到非扩张映射的不动点,并且该不动点还是某变分不等式的解.结果是新的,推广和改进了一些最新的结论. 相似文献
8.
本文将Schu关于Hilbert空间中渐近非扩张映射的迭代不动点定理推广到一致凸Banach空间。 相似文献
9.
该文在Banach空间里引进一种新的修改的Mann算法,来寻求一族无限个非扩张映射的公共元素.在适当条件下,得到了一个强收敛定理.所得结果改进和推广了许多最近的相关结果. 相似文献
10.
在一致光滑与2-一致凸Banach空间里,引进一个新的混合投影算法,找到了两族半相对非扩张映射的公共不动点集,有限个一般均衡问题的解集与宽松的协合算子的有限个变分不等式问题解集的公共元.所得结果推广了许多最近成果. 相似文献
11.
在Banach空间中引入渐近非扩张映象和非扩张映象某些类型的具误差的迭代序列,并研究了这些迭代序列的收敛性问题.本文的结果改进、推广和完善了最新的一些结果. 相似文献
12.
13.
14.
New monotone hybrid algorithm for hemi-relatively nonexpansive mappings and maximal monotone operators 总被引:1,自引:0,他引:1
The purpose of this article is to prove the strong convergence theorems for hemi-relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems for hemi-relatively nonexpansive mappings, a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi-relatively nonexpansive mappings. Noting that, the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi-relatively nonexpansive mappings. However, this new monotone hybrid algorithm can be used for hemi-relatively nonexpansive mappings. In addition, a new method of proof has been used in this article. That is, by using this new monotone hybrid algorithm, we firstly claim that, the iterative sequence is a Cauchy sequence. The results of this paper modify and improve the results of Matsushita and Takahashi, and some others. 相似文献
15.
In this paper, we introduce a new iterative scheme to investigate the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a relaxed cocoercive mapping by viscosity approximate methods. Our results improve and extend the recent ones announced by Chen et al. [J.M. Chen, L.J. Zhang, T.G. Fan, Viscosity approximation methods for nonexpansive mappings and monotone mappings, doi:10.1016/j.jmaa.2006.12.088], Iiduka and Tahakshi [H. Iiduka, W. Takahashi, Strong convergence theorems for nonexpansive mappings and inverse-strongly monotone mappings, Nonlinear Anal. 61 (2005) 341–350], Yao and Yao [Y.H. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput, doi:10.1016/j.amc.2006.08.062] and Many others. 相似文献
16.
Wataru Takahashi Yukio Takeuchi 《Journal of Mathematical Analysis and Applications》2008,341(1):276-286
In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space. 相似文献
17.
Weerayuth Nilsrakoo 《Applied mathematics and computation》2009,214(2):595-606
This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems. This new condition is implied by many previous known conditions introduced by many authors. We also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by Song-Chen, Kimura-Takahashi, Tan-Xu, and many others. 相似文献
18.
19.
In this paper, we introduce a new three-step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution. We show that the sequence converges strongly to a common element of two sets under some control conditions. Results proved in this paper may be viewed as an improvement and refinement of the recent results of Noor and Huang [M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press] and Yao and Yao [Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press]. 相似文献