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ISHIKAWA TYPE ITERATIVE SEQUENCES WITH ERRORS FOR LIPSCHITZIAN φ-STRONGLY ACCRETIVE OPERATOR EQUATIONS IN ARBITRARY BANACH SPACES 被引量:2
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作者 曾六川 《Numerical Mathematics A Journal of Chinese Universities(English Series)》 SCIE 2002年第1期25-33,共9页
In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iter... In this paper, we investigate the problem of approximating solutions of the equations of Lipschitzian ψ-strongly accretive operators and fixed points of Lipschitzian ψ-hemicontractive operators by lshikawa type iterative sequences with errors. Our results unify, improve and extend the results obtained previously by several authors including Li and Liu (Acta Math. Sinica 41 (4)(1998), 845-850), and Osilike (Nonlinear Anal. TMA, 36(1)(1999), 1-9), and also answer completely the open problems mentioned by Chidume (J. Math. Anal. Appl. 151 (2)(1990), 453-461). 展开更多
关键词 φ-strongly accretive operator φ-hemicontractive operator ishikawa type iterative sequences with errors
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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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CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES 被引量:3
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作者 TIAN You-xian(田有先) +1 位作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第9期1001-1008,共8页
Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding r... Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces. 展开更多
关键词 convex metric space fixed point generalized ishikawa (Mann) iterative sequence with errors general quasi-contractive mapping
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MANN AND ISHIKAWA ITERATIVE APPROXIMATION OF SOLUTIONS FOR m-ACCRETIVE OPERATOR EQUATIONS 被引量:1
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第12期1310-1318,共9页
The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors... The purpose of this paper is to study the Mann and Ishikawa iterative approximation of solutions for m_accretive operator equations in Banach spaces. The results presented in this paper extend and improve some authors' recent results. 展开更多
关键词 m _accretive operator Mann iterative sequence ishikawa iterative sequence
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SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES
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作者 ZHANG Shi-sheng(张石生) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第4期394-408,共15页
Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, ... Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results. 展开更多
关键词 accretive mapping pseudo-contractive mapping hemi-accretive mapping hemi-pseudo-contractive mapping ishikawa iterative sequence Mann iterative sequence steepest descent sequence
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ISHIKAWA ITERATIVE PROCESS FOR CONSTRUCTING SOLUTIONS OF m-ACCRETIVE OPERATOR EQUATIONS
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作者 ZENG Liu-chuan(曾六川) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2002年第6期686-693,共8页
The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschi... The convergence of the Ishikawa iteration sequences with errors for constructing solutions of m-accretive operator equations is characterized. Moreover, the error estimates of approximate solutions for locally Lipschitzian and m-accretive operator equations are established. 展开更多
关键词 m-accretive operator ishikawa iterative sequence uniformly smooth Banach space
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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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ITERATIVE PROCESS FOR CERTAIN NONLINEAR MAPPINGS WITH LIPSCHITZ CONDITION
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作者 GU Feng(谷峰) 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第12期1458-1467,共10页
Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive m... Using the new analysis techniques, the problem of iterative approximation of solutions of the equation for Lipschitz phi-strongly accretive operators and of fixed points for Lipschitz phi-strongly pseudo-contractive mappings are discussed. The main results of this paper improve and extend the corresponding results obtained by Chang, Chidume, Deng, Ding, Tan-Xu and Osilike. 展开更多
关键词 phi-strongly accretive operator phi-strongly pseudo-contractive mapping ishikawa iterative sequence Mann iterative sequence
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ITERATIVE PROCESS TO -HEMICONTRACTIVE OPERATOR AND-STRONGLY ACCRETIVE OPERATOR EQUATIONS
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作者 丁协平 张红琳 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第11期1256-1263,共8页
Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n b... Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E. Let T:K→K be a uniformly continuous _hemicontractive operator with bounded range and a n,b n,c n,a ′ n,b ′ n,c ′ n be sequences in [0,1] satisfying:ⅰ) a n+b n+c n=a ′ n+b ′ n+c ′ n=1. n≥0; ⅱ) lim b n= lim b ′ n= lim c ′ n= 0; ⅲ)∑∞n=0b n=∞; ⅳ) c n=o(b n). For any given x 0,u 0,v 0∈K, define the Ishikawa type iterative sequence x n as follows: x n+1 =a nx n+b nTy n+c nu n, y n=a ′ nx n+b ′ nTx n+c ′ nv n (n≥0), where u n and v n are bounded sequences in K. Then x n converges strongly to the unique fixed point of T. Related result deals with the convergence of Ishikawa type iterative sequence to the solution of _strongly accretive operator equations. 展开更多
关键词 strongly accretive operator _hemicontrictive operator ishikawa type iterative sequence Banach space
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Convergence of Iterative Sequence with Mixed Errors for Uniformly Quasi-Lipschitzian Mappings
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作者 张勇 《Journal of Southwest Jiaotong University(English Edition)》 2005年第2期185-188,共4页
In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special c... In convex metric spaces, the sufficient and necessary conditions for Ishikawa iterative sequences of uniformly quasi-Lipschitzian mapping T with mixed errors to converge to a fixed point ate proved, and as a special case, in which T need not be continuous. The results of this paper improve and extend some recent results. 展开更多
关键词 Convex metric space Uniformly quasi-Lipschitzian mapping ishikawa iterative sequence with mixed eroors Fixed point
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On the Characteristics of the Convergence of Ishikawa Type Iterative Sequences for Strong Pseudocontractions and Strongly Accretive Operators
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作者 曾六川 《Journal of Mathematical Research and Exposition》 CSCD 北大核心 2003年第3期403-409,共7页
In this paper, the results characterize the convergence of Ishikawa type iterative sequences (with errors) for constructing the solutions of strongly accretive operator equations, the solutions of rn-accretive operato... In this paper, the results characterize the convergence of Ishikawa type iterative sequences (with errors) for constructing the solutions of strongly accretive operator equations, the solutions of rn-accretive operator equations, and the fixed points of strong pseudocontractions. These results extend and improve Theorems 1-3 of Chidume and Osilike (Nonlinear Anal. TMA, 1999, 36(7): 863-872). 展开更多
关键词 ishikawa type iterative sequences strong pseudocontractions strongly accretive operators arbitrary Banach spaces.
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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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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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EXISTENCE AND APPROXIMATION OF SOLUTIONS TO VARIATIONAL INCLUSIONS WITH ACCRETIVE MAPPINGS IN BANACH SPACES
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作者 张石生 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2001年第9期997-1003,共7页
The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent res... The purpose of this paper is to study the existence and approximation problem of solutions for a class of variational inclusions with accretive mappings in Banach spaces. The results extend and improve some recent results. 展开更多
关键词 variational inclusion accretive mapping Mann(ishikawa) iterative sequence with errors
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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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