We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-st...We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.展开更多
The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also inclu...The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also included to explain the effectiveness of the proposed methods. The results of this paper are interesting extensions of those known results.展开更多
Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudaf...Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.展开更多
The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictl...The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property （K）. The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.展开更多
在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takaha...在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takahashi、2009年Qin X L,Cho Y Je和Kang S M等人的相应新结果.展开更多
文摘We introduce a general iterative method for a finite family of generalized asymptotically quasi- nonexpansive mappings in a hyperbolic space and study its strong convergence. The new iterative method includes multi-step iterative method of Khan et al. [1] as a special case. Our results are new in hyperbolic spaces and generalize many known results in Banach spaces and CAT(0) spaces, simultaneously.
基金The NSF(11071053)of ChinaNatural Science Basic Research Plan(2014JM2-1003)in Shaanxi Province of ChinaScientific Research Project(YD2016-12)of Yan’an University
文摘The purpose of this article is to propose a new hybrid projection method for a quasi-nonexpansive mapping. The strong convergence of the algorithm is proved in real Hilbert spaces. A numerical experiment is also included to explain the effectiveness of the proposed methods. The results of this paper are interesting extensions of those known results.
基金supported by National Natural Science Foundation of China(61503385)Fundamental Research Funds for the Central Universities of China(3122016L002)
文摘Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms.
基金Supported by the National Natural Science Foundation of China (Grant No.10771050)the Scientific Research Program Funded by Shaanxi Provincial Education Department (Grant No.11JK0486)
文摘The purpose of this article is to propose a shrinking projection method and prove a strong convergence theorem for a family of quasi-φ-strict asymptotically pseudo-contractions. Its results hold in reflexive, strictly convex, smooth Banach spaces with the property （K）. The results of this paper improve and extend the results of Matsushita and Takahashi, Marino and Xu, Zhou and Gao and others.
文摘在一致光滑和2-一致凸Banach空间框架下,引入广义杂交投影算法,建立了该算法强收敛于3个集合(平衡问题的解集、变分不等式的解集和两闭拟φ-非扩张映射公共不动点集)的公共解的新结果.所得结果本质改进和推广了2005年Matsushita和Takahashi、2009年Qin X L,Cho Y Je和Kang S M等人的相应新结果.
基金The National Natural Science Foundation of China(61751217)the Natural Science Basic Research Plan in Shaanxi Province(2016JM6082)the Scientific Research Project of Yan’an Univer sity(YD2016-12)
