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An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces

Author: W. A. Kirk
Journal: Proc. Amer. Math. Soc. 107 (1989), 411-415
MSC: Primary 47H10; Secondary 47H09
MathSciNet review: 941325
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Abstract: A uniform transfinite iteration procedure for selecting fixed points of nonexpansive mappings is introduced. This procedure, which applies to arbitrary nonexpansive mappings in Banach spaces having Kadec-Klee norm and to strictly contractive mappings in reflexive Banach spaces, is used to generalize a fixed point theorem of Kirk and Sternfeld for nonexpansive mappings in product spaces.

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  • [1] F. E. Browder, Semicontractive and semiaccretive nonlinear mappings in Banach spaces, Bull. Amer. Math. Soc. 74 (1968), 660-665. MR 0230179 (37:5742)
  • [2] D. van Dulst and B. Sims, Fixed points of nonexpansive mappings and Chebyshev centers in Banach spaces with norms of type (KK), in Banach Space Theory and its Applications, Lecture Notes in Mathematics No. 991, Springer Verlag, Berlin, New York, 1983. MR 714171 (84i:46027)
  • [3] R. E. Huff, Banach spaces which are nearly uniformly convex, Rocky Mountain J. Math. 10 (1980), 743-749. MR 595102 (82b:46016)
  • [4] S. Ishikawa, Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65-71. MR 0412909 (54:1030)
  • [5] J. L. Kelley, General topology, D. Van Nostrand Co., New York, 1965. MR 0070144 (16:1136c)
  • [6] W. A. Kirk and Y. Sternfeld, The fixed point property for nonexpansive mappings in certain product spaces, Houston J. Math. 10 (1984), 207-214. MR 744905 (85j:47058)
  • [7] W. A. Kirk and C. Martinez Yanez, Nonexpansive and locally nonexpansive mappings in product spaces, Nonlinear Analysis-TMA 12 (1988), 719-725. MR 947884 (89h:47084)
  • [8] B.-L. Lin, S. L. Troyanski, and Wenyao Zhang, On the points of continuity and the points of sequential continuity.

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Keywords: Nonexpansive mappings, fixed points, product spaces
Article copyright: © Copyright 1989 American Mathematical Society

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