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

Authors:
Lu-Chuan Ceng;Sy-Ming Guu;Jen-Chih Yao
Affiliations:
Department of Mathematics, Shanghai Normal University, Shanghai 200234, China;Department of Business Administration, College of Management, Yuan-Ze University, Chung-Li City, Taoyuan Hsien, 330, Taiwan;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 804, Taiwan
Venue:
Computers & Mathematics with Applications
Year:
2009

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Abstract

Consider on a real Hilbert space H a nonexpansive mapping T with a fixed point, a contraction f with coefficient 00, respectively. Let 0=1, with @m"n-@m(n-~), and prove the strong convergence of the iterative algorithm to a fixed point x@?@?Fix(T)@?C which is the unique solution of the variational inequality (for short, V I(A-I+@m(B-@cf),C)): =0,@?x@?C. 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 x"0@?H. The sequence {x"n} is proven to converge strongly to an element of C which is the unique solution x^* of the V I(A-I+@m(B-@cf),C). Applications to constrained generalized pseudoinverses are included.