利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

K·库玛; B·K·沙玛

利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

皮特·莱维桑卡苏克拉大学数学研究院,赖普_492010,印度

详细信息

作者简介:
B·K·沙玛,教授(联系人.Email:sharmabk_nib@sancharnet.in).

中图分类号: O177.91
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出版历程
- 收稿日期: 2004-09-12
- 刊出日期: 2005-11-15

Bruck Formula for a Perturbed Lipschitzian Iteration of Lipschitz Pseudocontractive Maps

School of Studies in Mathematics, Pt. Ravishankar Shukla University, Raipur, Chhattisgarh-492010, India

摘要

摘要: 在非线性分析中,处理伪紧缩算子及其变形的解（不动点）存在性和近似性，从而使演化方程的求解已经发展成为一个独立的理论．使用近似不动点技术，采用摄动迭代方法，目的是证明利普希茨伪紧缩映射序列的收敛性．该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况．推广了Chidume和Zegeye的结果．
- 伪紧缩映射 /
- 利普希茨摄动迭代 /
- 不动点 /
- 一致Gateaux微分范数
Abstract: The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution(fixed point) of pseudocontractive operators and its variants.The object is to introduce a perturbed iteration method for proving the convergence of sequence of Lipschitzian pseudocontractive mapping using approximate fixed point technique.This iteration can be ued for nonlinear operators which are more general than Lipschitzian pseudocontractive operator and Bruck iteration fails for proving their convergence.Our results generalize the results of Chidume and Zegeye.
- pseudocontractive map /
- perturbed Lipschitzian iteration /
- fixed point /
- uniformaly Gateaux differential norm

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参考文献(28)

[1]	Browder F E.Nonlinear mappings of nonexpansive and accretive type in Banach space[J].Bull Amer Math Soc,1967,73:875—882. doi: 10.1090/S0002-9904-1967-11823-8
[2]	Zeidler E.Nonlinear Functional Analysis and its Applications[M].Part-Ⅱ A;Linear Monotone Operater;Part Ⅱ B;Nonlinear Monotone Operators,(Berlin/New York:Springer Verlag),1985.
[3]	Chidume C E,Moore C.The solution by iteration of nonlinear equation in uniformly smooth Banach space[J].J Math Anal Appl,1997,215：132—146. doi: 10.1006/jmaa.1997.5628
[4]	Mann W R.Mean values methods in iteration[J].Proc Amer Math Soc,1953,4:506—510. doi: 10.1090/S0002-9939-1953-0054846-3
[5]	Osilike M O.Iterative solution of nonlinear equations of the -strongly accretive type[J].J Math Anal Appl,1996,200：259—271. doi: 10.1006/jmaa.1996.0203
[6]	Qihou L.The convergence theorems of the sequences of Ishikawa iterates for hemicontractive mappings[J].J Math Anal Appl,1990,148：55—62. doi: 10.1016/0022-247X(90)90027-D
[7]	Riech S.Iterative methods for accretive sets[A].In:Nonlinear Equation in Abstract Spacs[C].New York:Academic Press,1978，317—326.
[8]	张石生.Φ-伪压缩型映象的具误差的Ishikawa和Mann迭代程序的收敛性问题[J].应用数学和力学，2000，21(1)：1—10.
[9]	Geobel K.On the structure of minimal invarient sets for non-expansive mappings[J].Ann Univ Marie Curie-Sklodowska,1975,29:73—77.
[10]	Karlovitz L A.On nonexpansive mappings[J].Proc Amer Math Soc,1976,55:321—325. doi: 10.1090/S0002-9939-1976-0405182-X
[11]	Ray W O.Nonexpansive mappings on unbounded convex domains[J].Bull Acad Polon Sci Ser Math Astronorm Phys,1978,26：241—245.
[12]	Ray W O.The fixed point property and unbounded sets in Hlbert space[J].Trans Amer Math Soc,1980,258:531—537. doi: 10.1090/S0002-9947-1980-0558189-1
[13]	Simeon Reich.The almost fixed point property for nonexpansive mappings[J].Proc Amer Math Soc,1983,88:44—46. doi: 10.1090/S0002-9939-1983-0691276-4
[14]	Petryshyn W V.Construction of fixed points of demicompact mappings in Hilbert space[J].J Math Anal Appl,1966,14：276—284. doi: 10.1016/0022-247X(66)90027-8
[15]	Chidume C E.On the approximation of fixed points of non-expansive mappings[J].Houston J Math,1981,7:345—355.
[16]	Chidume C E,Mutangadura S A.An example on the Mann iteration method for Lipschitz pseudocontractions[J].Proc Amer Math Soc,2001,129:2359—2363. doi: 10.1090/S0002-9939-01-06009-9
[17]	Rhoades B E.Comments on two fixed point iteration methods[J].J Math Anal Appl,1976,56：741—750. doi: 10.1016/0022-247X(76)90038-X
[18]	Bruck R E Jr.A strongly convergent iterative method for the solution of 0∈U(x)for a maximal monotone opeartor U in Hilbert space[J].J Math Anal Appl,1974,48：114—126. doi: 10.1016/0022-247X(74)90219-4
[19]	Chidume C E,Zegeye H.Approximate fixed point sequences and convergence theorems for lipschitz pseudocontractive maps[J].Proc Amer Math Soc,2003,132(3):831—840.
[20]	Halpern B.Fixed points of nonexpanding maps[J].Bull Amer Math Soc,1967,73:957—961. doi: 10.1090/S0002-9904-1967-11864-0
[21]	Kato T.Nonlinear semigroups and evolution eauations[J].J Math Soc Japan,1967,19:508—520. doi: 10.2969/jmsj/01940508
[22]	Morales C H,Jung J S.Convergence of paths for pseudocontractive mappings in Banach spaces[J].Proc Amer Math Soc,2000,128:3411—3419. doi: 10.1090/S0002-9939-00-05573-8
[23]	Moore C,Nnoli B V C.Iterative solution of nonlinear equations involving set-valued uniformly accretive operators[J].Comput Math Appl,2001,42:131—140 doi: 10.1016/S0898-1221(01)00138-9
[24]	Ishiukawa S.Fixed points by a new iteration method[J].Proc Amer Math Soc,1974,44(1):147—150. doi: 10.1090/S0002-9939-1974-0336469-5
[25]	Ishiukawa S.Fixed points and iteration of a nonexpansive mapping in a Banach space[J].Proc Amer Math Soc,1976,59(1):65—71. doi: 10.1090/S0002-9939-1976-0412909-X
[26]	Lim T C,Xu H K.Fixed point theorems for asmptotically nonexpansive mappings[J].Nonlinear Anal TMA,1994,22:1345—1355. doi: 10.1016/0362-546X(94)90116-3
[27]	Qihou L.Iterative sequences for asymptotically quasinonexpansive mappings[J].J Math Anal Appl,2001,259：1—7. doi: 10.1006/jmaa.2000.6980
[28]	Krasnoselskij M A.Two remarks on the method of successive approximations[J].Uspchi Mat Nauk,1955,10:123—127.