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Search Results: 1 - 10 of 78220 matches for " Rudong Chen "
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Iterative Schemes for Fixed Point Computation of Nonexpansive Mappings
Rudong Chen
Abstract and Applied Analysis , 2012, DOI: 10.1155/2012/469270
Abstract: Fixed point (especially, the minimum norm fixed point) computation is an interestingtopic due to its practical applications in natural science. The purpose of thepaper is devoted to finding the common fixed points of an infinite family of nonexpansivemappings. We introduce an iterative algorithm and prove that suggested schemeconverges strongly to the common fixed points of an infinite family of nonexpansivemappings under some mild conditions. As a special case, we can find the minimumnorm common fixed point of an infinite family of nonexpansive mappings.
Strong convergence of approximation fixed points for nonexpansive nonself-mapping
Rudong Chen,Zhichuan Zhu
International Journal of Mathematics and Mathematical Sciences , 2006, DOI: 10.1155/ijmms/2006/16470
Abstract: Let C be a closed convex subset of a uniformly smooth Banach space E, and T:C→E a nonexpansive nonself-mapping satisfying the weakly inwardness condition such that F(T)≠∅, and f:C→C a fixed contractive mapping. For t∈(0,1), the implicit iterative sequence {xt} is defined by xt=P(tf(xt)
Hybrid Steepest Descent Method with Variable Parameters for General Variational Inequalities
Yu Yanrong,Chen Rudong
Journal of Inequalities and Applications , 2007,
Abstract: We study the strong convergence of a hybrid steepest descent method with variable parameters for the general variational inequality (GVI) . Consequently, as an application, we obtain some results concerning the constrained generalized pseudoinverse. Our results extend and improve the result of Yao and Noor (2007) and many others.
Hybrid Steepest Descent Method with Variable Parameters for General Variational Inequalities
Yanrong Yu,Rudong Chen
Journal of Inequalities and Applications , 2007, DOI: 10.1155/2007/19270
Abstract: We study the strong convergence of a hybrid steepest descent method with variable parameters for the general variational inequality (GVI) (F,g,C). Consequently, as an application, we obtain some results concerning the constrained generalized pseudoinverse. Our results extend and improve the result of Yao and Noor (2007) and many others.
An approximation method for continuous pseudocontractive mappings
Song Yisheng,Chen Rudong
Journal of Inequalities and Applications , 2006,
Abstract: Let be a closed convex subset of a real Banach space , is continuous pseudocontractive mapping, and is a fixed -Lipschitzian strongly pseudocontractive mapping. For any , let be the unique fixed point of . We prove that if has a fixed point and has uniformly Gateaux differentiable norm, such that every nonempty closed bounded convex subset of has the fixed point property for nonexpansive self-mappings, then converges to a fixed point of as approaches to 0. The results presented extend and improve the corresponding results of Morales and Jung (2000) and Hong-Kun Xu (2004).
Iterative Algorithm for Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces
Yonghong Yao,Rudong Chen
Fixed Point Theory and Applications , 2007, DOI: 10.1155/2007/32870
Abstract: We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.
Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups
He Huimin,Chen Rudong
Fixed Point Theory and Applications , 2007,
Abstract: Motivated by T. Suzuki, we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and improve the corresponding results of Kazuhide Nakajo and Wataru Takahashi (2003).
Hybrid methods for accretive variational inequalities involving pseudocontractions in Banach spaces
Wang Yaqin,Chen Rudong
Fixed Point Theory and Applications , 2011,
Abstract: We use strongly pseudocontractions to regularize a class of accretive variational inequalities in Banach spaces, where the accretive operators are complements of pseudocontractions and the solutions are sought in the set of fixed points of another pseudocontraction. In this paper, we consider an implicit scheme that can be used to find a solution of a class of accretive variational inequalities. Our results improve and generalize some recent results of Yao et al. (Fixed Point Theory Appl, doi:10.1155/2011/180534, 2011) and Lu et al. (Nonlinear Anal, 71(3-4), 1032-1041, 2009). 2000 Mathematics subject classification 47H05; 47H09; 65J15
Iterative Algorithm for Approximating Solutions of Maximal Monotone Operators in Hilbert Spaces
Yao Yonghong,Chen Rudong
Fixed Point Theory and Applications , 2007,
Abstract: We first introduce and analyze an algorithm of approximating solutions of maximal monotone operators in Hilbert spaces. Using this result, we consider the convex minimization problem of finding a minimizer of a proper lower-semicontinuous convex function and the variational problem of finding a solution of a variational inequality.
Strong Convergence Theorems of the CQ Method for Nonexpansive Semigroups
Huimin He,Rudong Chen
Fixed Point Theory and Applications , 2007, DOI: 10.1155/2007/59735
Abstract: Motivated by T. Suzuki, we show strong convergence theorems of the CQ method for nonexpansive semigroups in Hilbert spaces by hybrid method in the mathematical programming. The results presented extend and improve the corresponding results of Kazuhide Nakajo and Wataru Takahashi (2003).
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