On the Convergence of Iterative Processes for Generalized Strongly Asymptotically ϕ-Pseudocontractive Mappings in Banach Spaces

We prove the equivalence and the strong convergence of iterative processes involving generalized strongly asymptotically 𝜙-pseudocontractive mappings in uniformly smooth Banach spaces.

[1]  Tosio Kato,et al.  Nonlinear semigroups and evolution equations , 1967 .

[2]  S. S. Chang,et al.  Some results for asymptotically pseudo-contractive mappings and asymptotically nonexpansive mappings , 2000 .

[3]  Zhenyu Huang.  Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumptions , 2007 .

[4]  P. Maingé.  Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces , 2007 .

[5]  Yuguang Xu,et al.  Ishikawa and Mann Iterative Processes with Errors for Nonlinear Strongly Accretive Operator Equations , 1998 .

[6]  W. A. Kirk,et al.  A fixed point theorem for transformations whose iterates have uniform Lipschitz constant , 1973 .

[7]  Fanwei Bu,et al.  The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption , 2007 .

[8]  H. Zegeye,et al.  Approximate fixed point sequences and convergence theorems for Lipschitz pseudocontractive maps , 2003 .

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

[10]  Lishan Liu,et al.  Ishikawa and Mann Iterative Process with Errors for Nonlinear Strongly Accretive Mappings in Banach Spaces , 1995 .

[11]  S. S. Changa,et al.  On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings , 2005 .

[12]  C. O. Chidume,et al.  Convergence theorem for zeros of generalized Lipschitz generalized phi-quasi-accretive operators , 2005 .

[13]  F. Browder,et al.  NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[14]  H. Zhou,et al.  Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces☆ , 2009 .

[15]  William A. Kirk,et al.  A FIXED POINT THEOREM FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS , 1972 .

[16]  M. O. Osilike,et al.  Iterative Solution of Nonlinear Equations of the Φ-Strongly Accretive Type , 1996 .

[17]  Feng Gu,et al.  The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings , 2007 .

[18]  Billy E. Rhoades,et al.  The equivalence between Mann–Ishikawa iterations and multistep iteration , 2004 .

[19]  Chang He Xiang.  Fixed point theorem for generalized Φ -pseudocontractive mappings , 2009 .

[20]  F. Browder.  Nonlinear functional analysis , 1970 .

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

[22]  E. U. Ofoedu,et al.  Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space , 2006 .

[23]  Chi Kin Chan,et al.  On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings , 2006 .

[24]  Ştefan M. Şoltuz,et al.  The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps , 2004 .

[25]  Zhao-hong Sun,et al.  Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings , 2003 .

[26]  C. E. Chidume,et al.  Geometric Properties of Banach Spaces and Nonlinear Iterations , 2009 .

[27]  Felix E. Browder,et al.  Nonlinear mappings of nonexpansive and accretive type in Banach spaces , 1967 .

[28]  C. E. Chidume,et al.  EQUILIBRIUM POINTS FOR A SYSTEM INVOLVING M-ACCRETIVE OPERATORS , 2001, Proceedings of the Edinburgh Mathematical Society.