凸度量空间中拟压缩映象具误差的Ishikawa型迭代序列的收敛性

基金项目: 四川省教育厅自然科学重点科研项目(01LA70);国家自然科学基金资助项目(19771058)

Convergence of Ishikawa Type Iterative Sequence With Errors for Quasi-Contractive Mappings in Convex Metric Spaces

1.
Institute of Computer Science & Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, P. R. China;
2.
Department of Mathematics, Sichuan University, Chengdu 610064, P. R. China

摘要: 对凸度量空间中非线性拟压缩映象具误差的Ishikawa型迭代序列的收敛性问题证明了几个新的收敛性定理,结果不仅改进和推广了L.B.Ciric,Q.H.Liu,H.E.Rhoades,H.K.Xu等人的相应结果,而且对Rhoades-Naimplally-Singh所提出的公开问题,在凸度量空间的框架下给出了肯定的答复.
- 凸度量空间 /
- 不动点 /
- 具误差的Ishikawa型迭代序列 /
- 一般的拟压缩映象
Abstract: Some convergence theorems of Ishikawa type iterative sequence with errors for nonline ar general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corre sponding results of L. B. Ciric, Q. H. Liu, H. E. Rho ades and H. K. Xu, at el but also give an affirmative answer to the open question of Rhoades-Naimpally-Singh in convex metric spaces.
- convex metric space /
- fixed point /
- gener alized Ishikawa (Mann) iterative sequence with errors /
- general qua sicontr active mapping

[1]	Chang Shi-sheng,Cho Y J,Jung J S,et al.Iterative approximations of fixed points and solutions for strongly accretive and strongly pseudo-contractive mappings in Banach spaces[J].J Math Anal Appl,1998,224(1):149-165.
[2]	Ciric L B.A generalization of Banach's contraction principle[J].Proc Amer Math Soc,1974,45(1):267-273.
[3]	Chidume C E.Convergence theorems for strongly pseudo-contractive and strongly accretive mappings[J].J Math Anal Appl,1998,228(1):254-264.
[4]	Chidume C E.Global iterative schemes for strongly pseudo-contractive maps[J].Proc Amer Math Soc,1998,126(9):2641-2649.
[5]	Rhoades H E.Convergence of an Ishikawa type iteration scheme for a generalized contraction[J].J Math Anal Appl,1994,185(2):350-355.
[6]	XU Hong-kun.A note on the Ishikawa iteration scheme[J].J Math Anal Appl,1992,167(2):582-587.
[7]	Rhoades H E.Comments on two fixed point iteration methods[J].J Math Anal Appl,1976,56(2):741-750.
[8]	Naimpally S A,Singh K I.Extensions of some fixed point theorems of Rhoades[J].J Math Anal Appl,1983,96(2):437-446.
[9]	LIU Qi-hou.On Naimpally and Singh's open questions[J].J Math Anal Appl,1987,124(1):157-164.
[10]	LIU Qi-hou.A convergence theorem of the sequence of Ishikawa iterates for quasi-contractive mappings[J].J Math Anal Appl,1990,146(2):301-305.
[11]	Takahashi W.A convexity in metric space and nonexpansive mappings Ⅰ[J].Kodai Math Sem Rep,1970,22(1):142-149.