Strong convergence of asymptotically pseudocontractive semigroup by viscosity iteration

In this paper, we study the strong convergence of viscosity iteration and modified viscosity iteration process for strongly continuous semigroup of uniformly Lipschitzian asymptotically pseudocontractive mappings.

[1]  Shih-Sen Chang,et al.  Some problems and results in the study of nonlinear analysis , 1997 .

[2]  A Tikhonov,et al.  Solution of Incorrectly Formulated Problems and the Regularization Method , 1963 .

[3]  Yisheng Song,et al.  Strong convergence theorems for nonexpansive semigroup in Banach spaces , 2008 .

[4]  Robert V. Kohn,et al.  Local minimisers and singular perturbations , 1989, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[5]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[6]  P. Lions,et al.  Viscosity solutions of Hamilton-Jacobi equations , 1983 .

[7]  O. Ladyzhenskaya,et al.  Local estimates for gradients of solutions of non-uniformly elliptic and parabolic equations , 1970 .

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

[9]  J. Lions.  Perturbations Singulières dans les Problèmes aux Limites et en Contrôle Optimal , 1973 .

[10]  W. Fleming,et al.  Risk-Sensitive Control on an Infinite Time Horizon , 1995 .

[11]  R. Newcomb.  VISCOSITY SOLUTIONS OF HAMILTON-JACOBI EQUATIONS , 2010 .

[12]  Jamie Simpson,et al.  A strong convergence theorem for contraction semigroups in Banach , 2008 .

[13]  Klaus Deimling,et al.  Zeros of accretive operators , 1974 .

[14]  Jacques Louis Lions,et al.  Contrôle des systèmes distribués singuliers , 1983 .

[15]  H. Attouch.  Variational convergence for functions and operators , 1984 .

[16]  F. Browder,et al.  FIXED-POINT THEOREMS FOR NONCOMPACT MAPPINGS IN HILBERT SPACE. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

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

[18]  C. Chidume.  Strong convergence theorems for fixed points of asymptotically pseudocontractive semi-groups , 2004 .

[19]  Hong-Kun Xu,et al.  AN IMPLICIT ITERATION PROCESS FOR NONEXPANSIVE MAPPINGS , 2001 .

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

[21]  Hong-Kun Xu.  Strong convergence of an iterative method for nonexpansive and accretive operators , 2006 .

[22]  Tomonari Suzuki,et al.  On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces , 2002 .

[23]  Yisheng Song,et al.  Convergence theorems of iterative algorithms for continuous pseudocontractive mappings , 2007 .

[24]  Xiao Nan Li,et al.  Strong convergence of modified Ishikawa iteration for a nonexpansive semigroup in Banach spaces , 2010 .

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

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

[27]  Simeon Reich,et al.  On the asymptotic behavior of nonlinear semigroups and the range of accretive operators II , 1981 .

[28]  Dante C. Youla,et al.  On deterministic convergence of iterations of relaxed projection operators , 1990, J. Vis. Commun. Image Represent..

[29]  Wataru Takahashi,et al.  Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space , 2007 .

[30]  Lei Deng,et al.  Convergence to Common Fixed Point for Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces , 2008, Int. J. Math. Math. Sci..

[31]  高橋 渉.  Nonlinear functional analysis : fixed point theory and its applications , 2000 .

[32]  T. Zolezzi,et al.  Well-Posed Optimization Problems , 1993 .

[33]  Shin Min Kang,et al.  Approximation of fixed points of pseudocontraction semigroups based on a viscosity iterative process , 2011, Appl. Math. Lett..

[34]  A. Moudafi.  Viscosity Approximation Methods for Fixed-Points Problems , 2000 .

[35]  Jürgen Schu,et al.  Iterative construction of fixed points of asymptotically nonexpansive mappings , 1991 .

[36]  S. Rais.  ON STRONG CONVERGENCE TO COMMON FIXED POINTS IN BANACH SPACES , 2009 .