Strong convergence results for nonself multimaps in Banach spaces

We prove strong convergence theorems for multimaps under mild conditions, which include Browder's convergence theorem as well as Reich's convergence theorem. We thus provide a partial answer to Jung's question.

[1]  Hong-Kun Xu,et al.  Remarks on multivalued nonexpansive mappings , 1995 .

[2]  W. Takahashi,et al.  Fixed point theorem for nonexpansive semigroup on Banach space , 1994 .

[3]  Wataru Takahashi,et al.  On Reich's strong convergence theorems for resolvents of accretive operators , 1984 .

[4]  Hong-Kun Xu Multivalued nonexpansive mappings in Banach spaces , 2001 .

[5]  S. Nadler Multi-valued contraction mappings. , 1969 .

[6]  Hong-Kun Xu,et al.  Approximating curves of nonexpansive nonself-mappings in Banach spaces , 1997 .

[7]  J. Jung Strong convergence theorems for multivalued nonexpansive nonself-mappings in Banach spaces , 2007 .

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

[9]  KI,et al.  Strong Convergence Theorems for Accretive Operators in Banach Spaces* , 2003 .

[10]  K. Deimling Multivalued Differential Equations , 1992 .

[11]  J. Jung,et al.  Strong convergence of approximating fixed points for nonexpansive nonself-mappings in Banach spaces , 1998 .

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

[13]  Abdul Latif,et al.  Fixed points of multivalued nonexpansive maps , 1991 .

[14]  V. Berinde Iterative Approximation of Fixed Points , 2007 .

[15]  W. Takahashi,et al.  Strong convergence theorems for nonexpansive nonself-mappings in Banach spaces , 1998 .

[16]  Naseer Shahzad,et al.  Fixed points of multimaps which are not necessarily nonexpansive , 2005 .

[17]  Hong-Kun Xu,et al.  Strong convergence theorems for nonexpansive nonself-mappings , 1995 .

[18]  Felix E. Browder,et al.  Convergence of approximants to fixed points of nonexpansive nonlinear mappings in banach spaces , 1967 .

[19]  G. Marino,et al.  Convergence of approximating fixed point sets , 1990, ANNALI DELL UNIVERSITA DI FERRARA.

[20]  Leonard D. Berkovitz,et al.  Review: V. Barbu and Th. Precupanu, Convexity and optimization in Banach spaces , 1980 .

[21]  Wataru Takahashi,et al.  Strong convergence of approximants to fixed points of nonexpansive nonself-mappings in Banach spaces , 1998 .

[22]  Teck-Cheong Lim A fixed point theorem for weakly inward multivalued contractions , 2000 .

[23]  Abdul Latif,et al.  Fixed points of nonexpansive type multivalued maps , 1987 .

[24]  W. Takahashi,et al.  Fixed Point Theorem for Nonexpansive Semigroups on Banach Space , 1994 .

[25]  I. Ciorǎnescu Geometry of banach spaces, duality mappings, and nonlinear problems , 1990 .