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
In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T i...In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.展开更多
This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussio...This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.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
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
Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menge...Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.展开更多
Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process...Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.展开更多
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
The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN...The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.展开更多
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
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
Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique s...Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).展开更多
In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive ...In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of H(.,.)- φ - η - accretive operator.展开更多
In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges...In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself. Our results improve and extend Theorem 4.1 and 4.2 of Tan and Xu by removing the restrion lim n→∞β n=0 or lim n→∞α n= lim n→∞β n=0 in their theorems. These also extend Theorems 1 and 2 of Deng to the p -uniformly smooth Banach space setting.展开更多
Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have...Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.展开更多
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
In the present paper, by virtue of new approch techniques, we obtain several mapping theorems involving compact perturbations of m—accretive operators.These results improve and extend the corresponding those obtained...In the present paper, by virtue of new approch techniques, we obtain several mapping theorems involving compact perturbations of m—accretive operators.These results improve and extend the corresponding those obtained by Kartsatos,Zhu, and Kartsatos and Mabry.展开更多
In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper imp...In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting.展开更多
In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm i...In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.展开更多
A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T....A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T.H. and Xu H.K in 2005展开更多
文摘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.
基金The project supported by the Science and Technology Development Fund of Shanghai Higher Learning
文摘In this paper, we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X. We prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator frow X to X, or to the unique fixed point of T when T is a Lipschitzian and strictly pseudocontractive mapping from a nonempty closed convex subset K of X into itself. Our results are the extension and improvements of the earlier and recent results in this field.
文摘This article is devoted to the regularization of nonlinear ill-posed problems with accretive operators in Banach spaces. The data involved are assumed to be known approximately. The authors concentrate their discussion on the convergence rates of regular solutions.
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Supported by the National Natural Science Foundation of China(11071108)the Natural Science Foundation of Jiangxi Province of China(2010GZS0147)
文摘Based on the topological degree for 1-set-contractive fields established in [11], we discuss the 1-set-contractive perturbation and the existence of zero points for nonlinear equations with accretive mappings in Menger PN-spaces and obtain some new results.
文摘Suppose that X is a real Banach space, H: X→X is a Lipschitz operator, T: X→X is a uniformly continuous operator with bounded range, and H+T is strongly accretive. Then the Ishikawa iteration process converges strongly to the unique solution of the equation Hx+Tx=f . This conclusion extends the corresponding results in recent papers.
文摘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.
文摘The purpose of this paper is to introduce the concept of accretive mapping in probabilistic normed space (PN space, in short) and to study the existence problem of solutions for equations with accretive mappings in PN space and some existence theorems are shown.
文摘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.
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.
文摘Let X be a real Banach space and A : X→ 2x a bounded uniformly continuous Φ-strongly accretive multivalued mapping. For any f ∈ X, Mann and Ishikawa iterative processes with errors converge strongly to the unique solution of Ax (?) f. The conclusion in this paper weakens the stronger conditions about errors in Chidume and Moore's theorem (J. Math. Anal. Appl, 245(2000), 142-160).
文摘In this paper, we generalize H(.,.) accretive operator introduced by Zou and Huang [1] and we call it H(.,.)- φ - η - accretive operator. We define the resolvent operator associated with H(.,.)- φ - η - accretive operator and prove its Lipschitz continuity. By using these concepts an iterative algorithm is suggested to solve a generalized variational-like inclusion problem. Some examples are given to justify the definition of H(.,.)- φ - η - accretive operator.
文摘In this paper, we investigate the Ishikawa iteration process in a p -uniformly smooth Banach space X . Motivated by Deng and Tan and Xu , we prove that the Ishikawa iteration process converges strongly to the unique solution of the equation Tx=f when T is a Lipschitzian and strongly accretive operator from X to X , or to the unique fixed point of T when T is a Lipschitzian and strictly pseudo contractive mapping from a bounded closed convex subset C of X into itself. Our results improve and extend Theorem 4.1 and 4.2 of Tan and Xu by removing the restrion lim n→∞β n=0 or lim n→∞α n= lim n→∞β n=0 in their theorems. These also extend Theorems 1 and 2 of Deng to the p -uniformly smooth Banach space setting.
文摘Let X be a real uniformly smooth Banach space and let T:D(T)(?)X→Xbe (?)-hemicontractive and locally bounded at its fixed point q∈F(T).Under somesuitable assumptions on the iteration parameters {αn}and{βn},we have proved thatthe Mann and Ishikawa iteration processes for T converge strongly to the unique fixedpoint q of T.Several related results deal with iterative solutions of nonlinear equationsinvolving (?)-strongly quasi-accretive operators.Our results extend and generalize thosecorresponding ones by Xu and Roach,Zhou and Jia and others.
基金NNSF of China(19801023)Teachiug and Research A ward Fund for Outstanding Young Teachers in Higher Edncation Institutions of MOE.Chinal.
文摘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).
文摘In the present paper, by virtue of new approch techniques, we obtain several mapping theorems involving compact perturbations of m—accretive operators.These results improve and extend the corresponding those obtained by Kartsatos,Zhu, and Kartsatos and Mabry.
文摘In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting.
文摘In this paper, we prove a strong convergence theorem for resolvents of accretive operators in a Banach space by the viscosity approximation method with a generalized contraction mapping. The proximal point algorithm in a Banach space is also considered. The results extend some very recent theorems of W. Takahashi.
基金Foundation item： the National Natural Science Foundation of China （No. 10771050）.
文摘A more general form of modified Mann iterations which converges strongly to a zero point of an m-accretive operator is given. The work in this paper is an extension and complement of the corresponding result of Kim T.H. and Xu H.K in 2005
