Banach空间中关于公共不动点的强收敛性定理.
Convergence theorems for common fixed point problems in Banach space
摘要
引入一个迭代过程,在Banach空间中强收敛于可数个闭相对半非扩张映射的公共不动点.
In this paper, We introduce iterative process, they converges strongly to a common element of a set of common xed points of countably innite family of closed relatively quasi - nonexpansive mappings in Banach space.
出处
《湖北师范学院学报(自然科学版)》
2013年第2期52-55,共4页
Journal of Hubei Normal University(Natural Science)
参考文献14
-
1Alber Ya I. Metric and generalized projection operators in Banach spaces: Properties and applications, In:A. G. Kartsatos (Ed). Theory and Applications of Nonlinear Operators of Accretive and Monotone Type [ M ]. Dekker:New York, 1996.
-
2Cioranescu I. Geometry of Banach spaces, Duality Mapping and Nonlinear Problems [ M ]. Amsterdam: Kluwer Academic publishers, 1990.
-
3Alber Ya I, Reich S. An iterative method for solving a class of nonlinear operator equations in Banach spaces, Panamer [J]. Math J,1994,4:39 -54.
-
4Butanriu D, Reich S, ZasIavski A J. Weak convergence of orbits of nonlinear operators in reflexive Banach spaces [ J ]. Numer Funct Anal Optim,2003,24 : 489 - 508.
-
5Zegeye H, Ofoedu E U, Shahzad N. Convergence theorems for equilibrium problem, variational inequality problem and countably infinite relatively quasi -nonexpansive mappings[ J]. Nonlinear Anal Hybird Systems ,2010 ,in press.
-
6Zegeye H. A hybrid iteration scheme for equilibrium problems, variational inequality problems and common fixed point problems in Banach spaces [ J ]. Nonlinear Analysis ,2010,72:2136 - 2146.
-
7Kamimura S, Takahashi W. Strong convergence of proximal - type algorithm in a Banach space[ J ]. SIAM J Optim,2002, 13:938 - 940.
-
8Peng J W, Yao J C. A new hybrid - extragradient method for generalized mixed equilibrium problems, fixed point problems and variational inequality problems [ J ]. Taiwan Residents J Math,2008,12 : 1401 - 1432.
-
9Yao Y, Liou Y C, Yao J C. New relaxed hybrid - extragradient method for fixed point problems, a general system of varia- tional in equality problems and generalized mixed equilibrium problems[ J ]. Optimization ,2010, (in press).
-
10Nadezhkina N, Takahashi W. Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings[ J]. J Optim Theory Appl,2006 ,128 :191 -201.
-
1陈丽君.关于非扩张映射有限族、变分包含及均衡问题的迭代方法[J].宁夏大学学报(自然科学版),2015,36(1):6-11. 被引量:2
-
2倪仁兴.含m-增生算子的非线性方程的迭代程序[J].浙江师范大学学报(自然科学版),2002,25(1):8-12.
-
3董华.赋β-范线性空间中两种映像的公共不动点的强收敛性定理[J].延安大学学报(自然科学版),2012,31(4):23-25.
-
4石惠敏,王元恒.2个渐近拟伪压缩型非自映像公共不动点的强收敛性定理[J].浙江师范大学学报(自然科学版),2013,36(4):396-400. 被引量:1
-
5陈东青,高改良,刘立红.关于非扩展映象的有限族的一个强收敛性定理[J].军械工程学院学报,2003,15(1):71-74.
-
6何振华,谷峰.一族非扩张非自映射的强收敛性定理[J].浙江师范大学学报(自然科学版),2007,30(4):395-398.
-
7于林.H-值Mixingales及其收敛性[J].三峡大学学报(人文社会科学版),1997,20(3):17-20.
-
8陈加伟,万仲平,赵烈济.可数族弱Bregman相对非扩展映像的收敛性分析[J].数学物理学报(A辑),2014,34(1):70-79. 被引量:1
-
9郝自军,陈加伟,张涛.相对非扩张映射和均衡问题的投影迭代算法(英文)[J].应用数学,2013,26(2):300-307.
-
10杨莉,赵福海.Banach空间中一致L-Lipschitz映象的强收敛定理[J].数学的实践与认识,2011,41(16):165-170.