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
The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The resul...The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.展开更多
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
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in...A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.展开更多
<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the ...<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.展开更多
The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbit...The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors.展开更多
Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn...Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn} converges strongly to the unique fixed point of S.展开更多
Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical meth...Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.展开更多
A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et ...A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.展开更多
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
Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k...Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k epsilon (0,1). Let {alpha(n)} and {beta(n)} be two real sequences in [0,1] satisfying: (i) alpha(n) --> 0 as n --> infinity (ii) beta(n) < k(1 - k)/L(1 + L), for all n greater than or equal to 0; (iii) Pi(infinity) alpha(n) = infinity Set Sx = f - Tx + x, For All x epsilon X. Assume that {u(n)}(n=0)(infinity) and {v(n)}(n=0)(infinity) be two sequences in X satisfying parallel to u(n) parallel to = o(alpha(n)) and nu(n) --> 0 as n --> infinity. For arbitrary x(0) epsilon X, the iteration sequence {x(n)} is defined by (IS)(I) {x(n+1) = (1 - alpha(n))x(n) + alpha(n)Sy(n) + u(n), {y(n) = (1 - beta(n)) x(n) + beta(n)Sx(n) + v(n) (n greater than or equal to 0) then {x(n)} converges strongly to the unique solution of the equation Tx = f. related result deals with iterative approximation of fixed points of phi-hemicontractive mappings.展开更多
Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E...Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.展开更多
The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable B...The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.展开更多
基金Foundation items:the National Ntural Science Foundation of China(19771058)the Natural Science Foundation of Education Department of Sichuan Province(01LA70)
文摘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.
文摘The purpose of this paper is to introduce the concept of Φ_pseudo contractive type mapping and to study the convergence problem of Ishikawa and Mann iterative processes with error for this kind of mappings. The results presented in this paper improve and extend many authors'recent results.
基金supported by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Educations of MOE,P.R.C.the National Natural Science Foundation of P.R.C.No.19801023
文摘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).
文摘A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.
基金This work was supported partially by the Teaching and Research Award Fund for Outstanding Young Teachers in Higher Education Institutions by Ministry of Educationthe Department Fund of Science and Technology in Shanghai Higher Education Institutionsthe Special Funds for Major Specialities by the Shanghai Education Committee.
文摘<正>Let 1＜ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0＜α≤b_n+c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~'+c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f.
基金the National Natural Science Foundation of China ( Grant No.1 9971 0 1 3)
文摘The general results on convergence of the Ishikawa iteration procedures with errors for Lipschitzian φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type is established in arbitrary Banach spaces. As the direct applications, some stability results of the Ishikawa iteration methods for φ strong pseudo contractions and nonlinear operator equations of φ strongly accretive type are also given. Our results in this paper improve and extend the recent results due to Osilike and other authors.
文摘Let X be a uniformly smooth real Banach space. tri T:X→X be a con-tinuous and strongly accretive operator. For a given f∈X,define S: X→X by 1)satisfying: Moreover, suppose that {Sxn} and {Syn} are bounded, then {Xn} converges strongly to the unique fixed point of S.
文摘Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.
基金The foundation project of Chengdu University of Information Technology (No.CRF200502)
文摘A new concept of generalized set-valued strongly accretive mappings in Banach spaces was given and some strong convergence theorems of Ishikawa and Mann iterative process with errors approximation methods by Huang et al. was proved. The results presented in this paper improve and extend the earlier results obtained by Huang et al.
基金Supported by the National Science Foundation of Yunnan Province(2 0 0 2 A0 0 58M)
文摘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.
基金Supported by the National Natural Science Foundation of China (10871200)
文摘In this article, we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d, random environments.
文摘Let X be a real Banach space with a uniformly convex dual X*. Let T: X a X be a Lipschitzian and strongly accretive mapping with a Lipschitzian constant L greater than or equal to 1 and a strongly accretive constant k epsilon (0,1). Let {alpha(n)} and {beta(n)} be two real sequences in [0,1] satisfying: (i) alpha(n) --> 0 as n --> infinity (ii) beta(n) < k(1 - k)/L(1 + L), for all n greater than or equal to 0; (iii) Pi(infinity) alpha(n) = infinity Set Sx = f - Tx + x, For All x epsilon X. Assume that {u(n)}(n=0)(infinity) and {v(n)}(n=0)(infinity) be two sequences in X satisfying parallel to u(n) parallel to = o(alpha(n)) and nu(n) --> 0 as n --> infinity. For arbitrary x(0) epsilon X, the iteration sequence {x(n)} is defined by (IS)(I) {x(n+1) = (1 - alpha(n))x(n) + alpha(n)Sy(n) + u(n), {y(n) = (1 - beta(n)) x(n) + beta(n)Sx(n) + v(n) (n greater than or equal to 0) then {x(n)} converges strongly to the unique solution of the equation Tx = f. related result deals with iterative approximation of fixed points of phi-hemicontractive mappings.
基金the National Natural Science Foundation of China under Grant No. 19801017 andthe Foundation for University Key Teacher by th
文摘Letq>1,and let E be a real q-uniformly smooth Banach space. Let T: E→E be a continuous φstrongly accretive operator.For a given f E,let x*denote the unique solution of the equation Tx=f.Define the operator H:E→E by Hx=f+x-Tx,and suppose that the range of H is bounded. for any x1 E let {xn}∞n=qin E be the Ishikawa iterative process defined by Under suitable comditions,the Ishikawa iterative process strongly converges to the unique solution of Tx=f.the related result deals with the problems that Ishikawa iterative process strongly converges to the unique fixed point of -hemicontractive mappings.These results generalize results of Osilike [2],Chidume[4,5]and Tan[10],Zeng[11]and several other results from the class of strongly assertive operators and the class of strongly pseudocontractive operators to the much more general class of -trongly accrtive and class of -hemicontractive maps.
基金Project supported by the Natural Science Foundation of Yibin University (No. 2011Z03)
文摘The purpose of this paper is to study the almost sure T-stability and convergence of Ishikawa-type and Mann-type random iterative algorithms for some kind of C-weakly contractive type random operators in a separable Banach space. Under suitable conditions, the Bochner integrability of random fixed points for this kind of random operators and the almost sure T-stability and convergence for these two kinds of random iterative algorithms are proved.
