Strong Convergence of Two Iterative Algorithms for Nonexpansive Mappings in Hilbert Spaces

We introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed algorithms strongly converge to a fixed point of a nonexpansive mapping .

[1]  Hong-Kun Xu,et al.  Robustness of Mann's algorithm for nonexpansive mappings , 2007 .

[2]  P. Lions.  Approximation de Points Fixes de Contractions , 1977 .

[3]  Huang Jianfeng,et al.  Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces , 2007 .

[4]  Heinz H. Bauschke.  The Approximation of Fixed Points of Compositions of Nonexpansive Mappings in Hilbert Space , 1996 .

[5]  P. L. Combettes,et al.  The Convex Feasibility Problem in Image Recovery , 1996 .

[6]  S. Reich.  Weak convergence theorems for nonexpansive mappings in Banach spaces , 1979 .

[7]  P.L. Combettes.  On the numerical robustness of the parallel projection method in signal synthesis , 2001, IEEE Signal Processing Letters.

[8]  S. Atsushiba.  VISCOSITY APPROXIMATION METHODS FOR FIXED POINTS PROBLEMS , 2011 .

[9]  Simeon Reich,et al.  Almost convergence and nonlinear ergodic theorems , 1978 .

[10]  R. Wittmann.  Approximation of fixed points of nonexpansive mappings , 1992 .

[11]  S. Reich,et al.  Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings , 1984 .

[12]  M. Birkner,et al.  Blow-up of semilinear PDE's at the critical dimension. A probabilistic approach , 2002 .

[13]  Richard J. Mammone,et al.  Image recovery by convex projections using a least-squares constraint , 1990 .

[14]  F. Browder,et al.  Construction of fixed points of nonlinear mappings in Hilbert space , 1967 .

[15]  C. Byrne,et al.  A unified treatment of some iterative algorithms in signal processing and image reconstruction , 2003 .

[16]  Tomonari Suzuki,et al.  Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces , 2005 .

[17]  Hong-Kun Xu.  VISCOSITY APPROXIMATION METHODS FOR NONEXPANSIVE MAPPINGS , 2004 .

[18]  S. Reich.  Strong convergence theorems for resolvents of accretive operators in Banach spaces , 1980 .

[19]  Wataru Takahashi,et al.  Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces , 1997 .

[20]  B. Halpern.  Fixed points of nonexpanding maps , 1967 .

[21]  Tomonari Suzuki,et al.  A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings , 2006 .

[22]  J. Jung.  Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces , 2006 .