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CONVERGENT PROBLEM OF ITERATIVE SEQUENCES FOR NONLINEAR MAPPINGS WITH ERROR MEMBERS IN BANACH SPACES 被引量:5
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作者 SunZhaohong NiYongqin HeChang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期81-89,共9页
In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are inv... In this paper,the approximation problems of Ishikawa iteration with errors of fixed points for asymptotically nonexpansive mappings and asymptotically pseudocontractive mappings in arbitrary real Banach spaces are investigated.Some necessary condition and sufficient condition for the convergence of iterative sequences are given respectively.The results thus extend and improve some recent corresponding results. 展开更多
关键词 asymptotically nonexpansive mapping asymptotically pseudocontractive mapping modified Ishikawa iterative sequence with errors arbitrary Banach space fixed point.
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ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED OINTS FOR ASYMPTOTICALLY NON-EXPANSIVE TYPE MAPPINGS IN BANACH SPACES 被引量:7
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第1期25-34,共10页
Some iterative approximation theorems of fixed points for asymptotically nonexpansive type mappings in Banach spaces are obtained.
关键词 asymptotically nonexpansive mapping fixed point modified Ishikawa iterative sequence with errors modified Mann iterative sequence with errors
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INTERATIVE APPROXIMATION OF FIXED POINTS FOR ALMOST ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES
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作者 曾六川 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2003年第12期1421-1430,共10页
A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces... A new class of almost asymptotically nonexpansive type mappings in Banach spaces is introduced,which includes a number of known classes of nonlinear Lipschitzian mappings and non_Lipschitzian mappings in Banach spaces as special cases; for example,the known classes of nonexpansive mappings,asymptotically nonexpansive mappings and asymptotically nonexpansive type mappings.The convergence problem of modified Ishikawa iterative sequences with errors for approximating fixed points of almost asymptotically nonexpansive type mappings is considered.Not only S.S.Chang's inequality but also H.K.Xu's one for the norms of Banach spaces are applied to make the error estimate between the exact fixed point and the approximate one.Moreover,Zhang Shi_sheng's method(Applied Mathematics and Mechanics(English Edition),2001,22(1):25-34) for making the convergence analysis of modified Ishikawa iterative sequences with errors is extended to the case of almost asymptotically nonexpansive type mappings. The new convergence criteria of modified Ishikawa iterative sequences with errors for finding fixed points of almost asymptotically nonexpansive type mappings in uniformly convex Banach spaces are presented. Also,the new convergence criteria of modified Mann iterative sequences with errors for this class of mappings are immediately obtained from these criteria.The above results unify,improve and generalize Zhang Shi_sheng's ones on approximating fixed points of asymptotically nonexpansive type mappings by the modified Ishikawa and Mann iterative sequences with errors. 展开更多
关键词 almost asymptotically nonexpansive type mapping fixed point modified Ishikawa iterative sequence with error modified Mann iterative sequence with error
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Modified Ishikawa Iterative Process with Errors in Normed Linear Spaces
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作者 姚永红 陈汝栋 周海云 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2007年第2期298-306,共9页
Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of (ψ)-hemicontractive mapping in normed l... Ishikawa iterative sequences with errors different from the iterative sequences introduced by Liu and Xu are given. Moreover, the problem of approximating the fixed points of (ψ)-hemicontractive mapping in normed linear spaces by the modified Ishikawa iterative sequences with errors is investigated. The results presented in this paper improve and extend the results of the others. 展开更多
关键词 (ψ)-hemicontractive mapping modified Ishikawa iterative sequences with errors fixed point normed linear spaces.
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Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings
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作者 Ze Qing LIU Shin Min KANG 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2004年第6期1009-1018,共10页
A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty ... A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991). 展开更多
关键词 Asymptotically non-expansive mapping Fixed point modified three-step iterative sequence with errors modified Ishikawa iterative sequence with errors Uniformly convex Banach space Opial’s condition Weak convergence Strong convergence
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