论文信息 - On Kirk’s strong convergence theorem for multivalued nonexpansive mappings on CAT(0) spaces

On Kirk’s strong convergence theorem for multivalued nonexpansive mappings on CAT(0) spaces

Abstract We prove a strong convergence theorem for multivalued nonexpansive mappings which includes Kirk’s convergence theorem on CAT(0) spaces. The theorem properly contains a result of Jung for Hilbert spaces. We then apply the result to approximate a common fixed point of a countable family of single-valued nonexpansive mappings and a compact valued nonexpansive mapping.

[1] P. Pietramala. Convergence of approximating fixed points sets for multivalued nonexpansive mappings , 1992 .

[2] W. A. Kirk,et al. Topics in Metric Fixed Point Theory , 1990 .

[3] Satit Saejung,et al. Halpern's Iteration in CAT(0) Spaces , 2009 .

[4] Sompong Dhompongsa,et al. Lim's theorems for multivalued mappings in CAT(0) spaces☆ , 2005 .

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

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

[7] M. Bridson,et al. Metric Spaces of Non-Positive Curvature , 1999 .

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

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

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

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

[12] Habtu Zegeye,et al. Strong convergence results for nonself multimaps in Banach spaces , 2007 .

[13] William A. Kirk,et al. A concept of convergence in geodesic spaces , 2008 .

[14] William A. Kirk,et al. Fixed points of uniformly lipschitzian mappings , 2006 .

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