Strong convergence theorems for strongly continuous semigroups of pseudocontractions

Abstract In this work, strongly continuous semigroups of pseudocontractions are studied based on an implicit iterative algorithm. Strong convergence theorems of fixed points are obtained in an arbitrary Banach space.

[1]  Haiyun Zhou,et al.  CONVERGENCE THEOREMS OF COMMON FIXED POINTS FOR A FINITE FAMILY OF LIPSCHITZ PSEUDOCONTRACTIONS IN BANACH SPACES , 2008 .

[2]  Isa Yildirim,et al.  On strong convergence in real Banach spaces obtained by dropping the Lipshitz condition , 2011, Appl. Math. Lett..

[3]  Yeol Je Cho,et al.  On the strong convergence of the implicit iterative processes with errors for a finite family of asymptotically nonexpansive mappings , 2008, Appl. Math. Lett..

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

[5]  Xiaolong Qin,et al.  Implicit iterative algorithms for treating strongly continuous semigroups of Lipschitz pseudocontractions , 2010, Appl. Math. Lett..

[6]  Y. Hao Convergence Theorems of Common Fixed Points for Pseudocontractive Mappings , 2008 .

[7]  Ravi P. Agarwal,et al.  Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme , 2011, Appl. Math. Lett..

[8]  Hong-Kun Xu,et al.  Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process , 1993 .

[9]  Shi-sheng Zhang Convergence theorem of common fixed points for Lipschitzian pseudo-contraction semi-groups in Banach spaces , 2009 .

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

[11]  M. O. Osilike,et al.  Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps , 2004 .

[12]  Rudong Chen,et al.  Strong convergence theorems for the implicit iteration process for a finite family of hemicontractive mappings in Banach space , 2009, Appl. Math. Lett..

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

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

[15]  S. Stević APPROXIMATING FIXED POINTS OF NONEXPANSIVE MAPPINGS , 2006 .