Lipschitz局部严格伪压缩映象的迭代逼近*
Iterative Process for Lipschitz Local Strictly Pseudocontractive Mappings
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摘要: 设K是一致光滑Banach空间K的非空子集,T:K→X是Lipschitz局部严格伪压缩映象。本文给出一个迭代序列强收敛到T的唯一不动点,并给出一个涉及Lipschitz局部强增殖映象T的非线性方程Tx=f的解的迭代逼近。
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关键词:
- 局部严格伪压缩 /
- 局部强增殖 /
- 一致光滑Banach空间
Abstract: Suppose that K is a non-empty subset of uniformly smooth Banach space X.Let T:K→X be a Lipschitz local strcily pseudocontractine mapping.In this paper,the iterative sequence which converges strongly to the unique fixed point of Tis given.A related result deals with the problem that the Ishikawa iteration process canverges strongly to a solution of the equation TX-f when T is Lipschitzian and local strongly accretive in X. -
[1] Chidume, C.E,Iterative approxim at ion of fined points of Lipschitzian strictly pseudocontractive mappings, Proc, Amer, Math, Soc,99(2)(1987).283-288. [2] Deng, L, and X, P, Ding, Iterative approximation of Lipschitz strictly pseudo-contractive mappings in uniformly smooth Banach spaces,(submitted) [3] Ishikawa, S.,Fixed points by a new iteration method,Proc, Amer, Math,Soc.,44(1974).147-150. [4] Kato, T,Nonlinear semigroups and evolution equations, J.Math, Soc,Japan, 19(1967),508-520. [5] Lindenstrauss, J, and L, Tsafriri, Classical Banach Spaces, I,Springer-Yerlag, New York/Berlin(1979). [6] Reich, S,An iterative proved ure for constructing zeros of accretive sets in Banach spaces, J, Nonlinear Anal.,(2)(1978),85-92. [7] Weng, X,Fixed point iteration for local strictly pseudo-contractive mapping,Proc, Amer, Math, Soc,113(1991), 727-731. [8] Xu, Z.B, and G, F, Roach, Characteristic inequalities of uniformly convex and uniformly smooth Banach spaces, J, Math, Anal, Appl.,167 (1991), 189-210.
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