The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Bana...The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].展开更多
In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseu...In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].展开更多
Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed poin...Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.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
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
Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β n...Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.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 stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space....The stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space. Under parameters satisfying certain conditions, the convergence of iterative sequences was proved. The results improve and extend the recent corresponding results, and supply the basis of theory for further discussing convergence of iteration procedures with errors.展开更多
This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-con...This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.展开更多
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
The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-stric...The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.展开更多
基金supported by the National Natural Science Foun-dation of China (11071169)the Natural Science Foundation of Zhejiang Province (Y6110287)
文摘The purpose of this paper is to study necessary and su？cient condition for the strong convergence of a new parallel iterative algorithm with errors for two finite families of uniformly L-Lipschitzian mappings in Banach spaces. The results presented in this paper improve and extend the recent ones announced by [2–7].
基金supported by Scientific Research Fund of Sichuan Provincial Education Department (09ZB102)Scientific Research Fund of Science and Technology Deportment of Sichuan Provincial (2011JYZ011)
文摘In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].
文摘Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.
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.
文摘Without the Lipschitz assumption and boundedness of K in arbitrary Banach spaces, the Ishikawa iteration ｛x n｝ ∞ n=1 defined byx 1∈K,\ x n+1 =(1-α n)x n+α nTy n,\ y n=(1-β n)x n+β nTx n,\ n≥1satisfying 0<α n,β n<1 ,for all n≥1;∑ ∞ n=1 α n=∞;α n→0,β n→0 as n→∞ is proved to converge strongly to the unique fixed point of T ,where T:K→K is a uniformly continuous strictly pseudo\|contractive operator with bounded range.
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 stability of the Ishikawa iteration procedures was studied for one class of continuity strong pseudocontraction and continuity strongly accretive operators with bounded range in real uniformly smooth Banach space. Under parameters satisfying certain conditions, the convergence of iterative sequences was proved. The results improve and extend the recent corresponding results, and supply the basis of theory for further discussing convergence of iteration procedures with errors.
文摘This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.
文摘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.
文摘The composite implicit iteration process introduced by Su and Li [J. Math. Anal. Appl. 320 (2006) 882-891] is modified. A strong convergence theorem for approximation of common fixed points of finite family of k-strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the modified iteration process.
