Banach空间中含强增生算子的非线性方程的迭代解

周海云

Banach空间中含强增生算子的非线性方程的迭代解

周海云

军械工程学院基础部, 石家庄 050003

详细信息

作者简介:
周海云(1958~ ),男,副教授,已在国内外重要杂志上发表论文38篇

中图分类号: O177.91
计量
- 文章访问数: 2227
- HTML全文浏览量: 101
- PDF下载量: 842
- 被引次数: 0
出版历程
- 收稿日期: 1997-04-28
- 修回日期: 1998-04-05
- 刊出日期: 1999-03-15

Iterative Solution of Nonlinear Equations with Strongly Accretive Operators in Banach Spaces

Zhou Haiyun

Department of Basic Science, Ordnance Engineering College, Shijiazhuang 050003, P. R. China

摘要

摘要: 设X为实Banach空间,X^*为其一致凸的共轭空间.设T:X→X为Lipschitzian强增生映象,L≥1为其Lipschitzian常数,k∈(0,1)为其强增生常数.设{α_n},{β_n}为[0,1]中的两个实数列满足:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ).假设为X中两序列满足:=o(β_n)与μ_n→0(n→∞).任取x₀∈X,则由(IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0){所定义的迭代序列{x_n强收敛于方程T
- 带误差的Ishikawa迭代 /
- 强增生映象 /
- φ-半压缩映象
Abstract: :Let X be a real Banach space with a uniformly convex dual X^*. Let T :X y X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L≥1 and a strongly accretive constant k∈(0,1). Let {α_n},{β_n}. be two real sequence in [0,1] satisfying:(ⅰ)α_n→0(n→∞);(ⅱ)β_n<L(1+L)/k(1-k)(n≥0);(ⅲ) Set Sx=f-Tx+x Assume that be two sequences in X satisfying =o(β_n)与μ_n→0(n→∞).For arbitrary x₀∈X the iteration sequence {x_n} is defined by IS)1x_n+1=(1-α_n)x_n+α_nSy_n+u_ny_n=(1-β_n)x_n+β_nSx_n+μ_n(_n≥0) then {x_n converges strongly to the unique solution of the equation Tx=f A related result deals with iterative approximation of fixed points of φhemicontractive mappings.
- Ishikawa iteration with errors /
- strongly accretive mapping /
- φ-hemicontractive mapping

HTML全文

参考文献(32)

[1]	Browder F E.Nonlinear operators and nonlinear equations of evolution in Banach spaces,[J].Proc Sympos Fure Math,1976,18
[2]	Barbu V.Nonlinear Semigroups and Differential Equations in Banach Spaces[M].Leyden,The Netherlands:Noordhoff Int Publ,1976
[3]	Kato T.Nonlinear semigroups and evolution equations[J].J Math Soc Japan,1967,19(18):508～520
[4]	Deimling K.Nonlinear Functional Analysis[M].New York／Berlin:Springer-Verlag,1985
[5]	Chidume C F.Iterative solution of nonlinear equations with strongly accretive operators[J].J Math Anal Appl,1995,195:502～518
[6]	Deng I,Ding Xieping.Iterative approximation of Lipschitz strictly pseudocontractive mappings in uniformly smooth Banach spaces[J].Nonlinear Anal,1995,24:981～987
[7]	Chidume C E.Steepest descent approximations for accretive operator equations[J].Nonl Anal,1996,26:299～311
[8]	Bruck R E.The iterative solution of the equation y∈x+Tx for a monotone operator T in Hilbcrt space,[J].Bull Amer Soc,1973,79:1258～1261
[9]	Ishikawa S.Fixed points by a new iteration method[J].Proc Amer Math Soc,1974,149:147～150
[10]	Zhou H Y,Jia Y T.Approximation of fixed points of strongly psrudocontractive maps without Lipschitz assumption[J].Proc Amer Math Soc.(to appear)
[11]	Zhou H Y,Jia Y T.Approximating the zeros of accretive operators by the Ishikawa iteration process[J].Abtr Appl Anal,1996,1(2):153～167
[12]	Zhou H Y.A remark on ishikawa iteration[J].Chinese Science Bulletin,1997,42:631～633
[13]	Osilike M O.Iterative solution of nonlinear equations of the -strongly accretive type[J].J Math Anal Appl,1996,200:259～271
[14]	Chidume C E.Iterative solutions of nonlinear equations in smooth Banach spaces[J].Nonl Anal,1996,26:1823～1834
[15]	Browder F E.Nonlinear mappings of nonexpansive and accretive type in Banach spaces[J].Bull Amer Math Soc,1967,73:875～882
[16]	Browder F E,Petryshyn W V.Contruction of fixed points of nonlinear mappings in Hilbert space[J].J Math Anal Appl,1967,20:197～228
[17]	Deimling K.Zeros of accretive operators,Manuscripta Math,1974,13:365～374
[18]	Chidume C E.Approximation of fixed points of strongly pscudocontractive mappings[J].Proc Amer Math Soc,1994,120:545～551
[19]	Chidume C E,Osilike M O.Fixed point iterations for strictly hemi-contractive maps in uniformly smooth Banach spaces[J].Numercal Funct Anal Optim,1994,15:779～790
[20]	Deng L.On Chidume's open qucstions[J].J Math Anal Appl,1993,174:441～449
[21]	Deng L.An iterative process for nonlinear Lipschitzian and strongly accretive mappings in uniformly convex and uniformly smooth Banach spaces[J].Acta Appl Math,1993,32:183～196
[22]	Zhou H Y.Iterative solutions of nonlinear equations involving strongly accretive operators without Lipschitz assumption[J].J Math Anal Appl,(to appear soon)
[23]	Wann W R.Mean value methods in iteration[J].Proc Amer Math Soc,1953,4:506～510
[24]	Rhoades B E.Commcnts on two fixed point iteration methods[J].J Math Anal Appl,1976,56:741～750
[25]	Reich S.An iterative procedure for constructing zeros of accretive sets in Banach spaces,[J].Nonlinear Anal,1978,2
[26]	Reich S.Constructive techniques for accretive and monotone operators[A].In:V.Lakshmikantham Ed.Appl Nonl Anal[M],New York:Academic Press,1979,335～345
[27]	Reich S.Constructing zers of accretive operators [J].Appl Anal,1979,9:159～163
[28]	Reich S,Strong convergence theorems for resolvents of accretive operators in Banach spaces[J].J Math Anal Appl,1980,85:287～292
[29]	You Z Y,Xu Z B.A class of iteration methods for a strongly monotone operator equation and application to finite element approximate solution of nonlinear elliptic boundary value problem[J].J Comput Math,1984,2:112～121
[30]	Xu Z B,Roach G F.A necessary and sufficient condition for convergence of steepest descent approximation to accretive operator equations[J].J Math Anal Appl,1991,167:189～210
[31]	Schu J.On a theorem of C E Chidume concerning the iterative approximation of fixed points [J].Math Nachr,1991,153:313～319
[32]	Schu J.Iterative construction of fixed points of strictly pseudocontractive mappings[J].Appl Anal,1991,40:67～72