In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the inte...In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.展开更多
Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by ...Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.展开更多
In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the mod...In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.展开更多
This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods...This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.展开更多
In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear ...In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.展开更多
In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactor...In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.展开更多
This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of none...This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.(Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715(2009)),Plubtieng and Punpaeng(Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469(2007)),Colao et al.(Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352(2008)),Yao et al.(Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363(2007)DOI 10.1155/2007/64363),and others.展开更多
The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper e...The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.展开更多
An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. ...An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.展开更多
This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. ...This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.展开更多
In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results...In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.展开更多
The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper exten...The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 (2008)], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 (2006)], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 (2001)] and Osilike [J. Math. Anal. Appl., 294, 73-81 (2004)]. Keywords展开更多
文摘In this paper,we introduce a three-step composite implicit iteration process for approximating the common fixed point of three uniformly continuous and asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.We prove that our proposed iteration process converges to the common fixed point of three finite family of asymptotically generalizedΦ-hemicontractive mappings in the intermediate sense.Our results extends,improves and complements several known results in literature.
文摘Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.
基金Scientific Research Fund of Zhejiang Provincial Education Department(No.20051778 and No.20051760)Scientific Research Fund of Ningbo University(200542)
文摘In this paper, we will establish several strong convergence theorems for the approximation of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.
基金This work was supported by the National Natural Science Foundation of China
文摘This paper discusses a kind of implicit iterative methods with some variable parameters, which are called control parameters, for solving ill-posed operator equations. The theoretical results show that the new methods always lead to optimal convergence rates and have some other important features, especially the methods can be implemented parallelly.
基金supported by the Key Disciplines of Shanghai Municipality (Operations Research & Cybernetics, No. S30104)the Shanghai Leading Academic Discipline Project (No. J50101)
文摘In the paper, we extend the implicit iterative method for linear ill-posed operator equations to solve nonlinear ill-posed problems. We show that under some conditions the error sequence of solutions of the nonlinear implicit iterative method is monotonically decreasing and, with this monotonicity, prove convergence of the new method for both the exact and perturbed equations.
文摘In this paper, the author applied an implicit iterative method to solve linear ill posed equations with both perturbed operators and perturbed data. After having carefully estimated some terms involved, a satisfactory order of convergence rate was derived.
基金supported by the Natural Science Foundation of Yibin University(No.2009Z3)
文摘This paper proposes a modified iterative algorithm using a viscosity approximation method with a weak contraction.The purpose is to find a common element of the set of common fixed points of an infinite family of nonexpansive mappings and the set of a finite family of equilibrium problems that is also a solution to a variational inequality.Under suitable conditions,some strong convergence theorems are established in the framework of Hilbert spaces.The results presented in the paper improve and extend the corresponding results of Colao et al.(Colao,V.,Acedo,G.L.,and Marino,G.An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings.Nonlinear Anal.71,2708–2715(2009)),Plubtieng and Punpaeng(Plubtieng,S.and Punpaeng,R.A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces.J.Math.Anal.Appl.336,455–469(2007)),Colao et al.(Colao,V.,Marino,G.,and Xu,H.K.An iterative method for finding common solutions of equilibrium problem and fixed point problems.J.Math.Anal.Appl.344,340–352(2008)),Yao et al.(Yao,Y.,Liou,Y.C.,and Yao,J.C.Convergence theorem for equilibrium problems and fixed point problems of infinite family of nonexpansive mappings.Fixed Point Theory Application 2007,Article ID 64363(2007)DOI 10.1155/2007/64363),and others.
基金supported by the Natural Science Foundation of Yibin University (No. 2007Z3)
文摘The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontractive semi-groups in the general Banach spaces. The results presented in this paper extend and improve the corresponding results of some people.
文摘An inverse problem for identification of the coefficient in heat-conduction equation is considered. After reducing the problem to a nonlinear ill-posed operator equation, Newton type iterative methods are considered. The implicit iterative method is applied to the linearized Newton equation, and the key step in the process is that a new reasonable a posteriori stopping rule for the inner iteration is presented. Numerical experiments for the new method as well as for Tikhonov method and Bakushikskii method are given, and these results show the obvious advantages of the new method over the other ones.
文摘This paper presents the implicit method of streamline iteration on the bases of the method of streamline itera- tion for computing two-dimensional viscous incompressible steady flow in a channel with arbitrary shape. A new total pressure equation of viscous incompressible flow is introduced in this paper and the equation is numerically computed by the implicit method. It is shown from the computational results of examples that the implicit method of streamline iteration can speed up the convergence and decrease the computational time.
文摘In this paper we propose a kind of implicit iterative methods for solving ill-posed operator equations and discuss the properties of the methods in the case that the control parameter is fixed. The theoretical results show that the new methods have certain important features and can overcome some disadvantages of Tikhonov-type regularization and explicit iterative methods. Numerical examples are also given in the paper, which coincide well with theoretical results.
基金Supported by Natural Science Foundation of Yibin University (Grant No. 2009Z3)
文摘The purpose of this paper is to study the weak convergence problems of the irnplicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results of Zhou [Nonlinear Anal., 68, 2977-2983 (2008)], Chen, et ah [J. Math. Anal. Appl., 314, 701 709 (2006)], Xu and Ori [Numer. Funct. Anal. Optim, 22, 767-773 (2001)] and Osilike [J. Math. Anal. Appl., 294, 73-81 (2004)]. Keywords