Hybrid viscosity-like approximation methods for nonexpansive mappings in Hilbert spaces

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• 作者：Lu-Chuan Ceng ; Sy-Ming Guu ; Jen-Chih Yao
• 关键词：Nonexpansive mapping ; Variational inequality ; Fixed point ; Hybrid viscosity-like approximation method ; Strong convergence ; Constrained generalized pseudoinverse
• 刊名：Computers and Mathematics with Applications
• 出版年：2009
• 出版时间：August 2009
• 年：2009
• 卷：58
• 期：3
• 页码：605-617
• 全文大小：770 K

文摘

Consider on a real Hilbert space H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 0<α<1, and two strongly positive linear bounded operators A,B with coefficients and β>0, respectively. Let 0<γα<β. We introduce a general iterative algorithm defined by with μ_n→μ(n→∞), and prove the strong convergence of the iterative algorithm to a fixed point which is the unique solution of the variational inequality (for short, ): . On the other hand, assume C is the intersection of the fixed-point sets of a finite number of nonexpansive mappings on H. We devise another iterative algorithm which generates a sequence {x_n} from an arbitrary initial point x₀H. The sequence {x_n} is proven to converge strongly to an element of C which is the unique solution x^* of the . Applications to constrained generalized pseudoinverses are included.