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Fixed point theorems for mappings of nonexpansive type


Author: Teck-Cheong Lim
Journal: Proc. Amer. Math. Soc. 66 (1977), 69-74
MSC: Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-1977-0473935-9
MathSciNet review: 0473935
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Abstract: Constructive fixed point theorems for single-valued and compact-valued nonexpansive mappings, which map a closed convex subset C of a Banach space X into X and send the boundary of C relative to X into C, are given. Mappings for which the method of asymptotic center applies are also considered.


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  • [1] N. A. Assad and W. A Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972), 553-562. MR 0341459 (49:6210)
  • [2] M. Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 44 (1974), 369-374. MR 0358451 (50:10917)
  • [3] K. Goebel and W. A Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 30 (1972), 171-174. MR 0298500 (45:7552)
  • [4] -, A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135-140. MR 0336468 (49:1242)
  • [5] R. C. James, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542-550. MR 0173932 (30:4139)
  • [6] W. A. Kirk, Fixed point theorem for nonlinear nonexpansive and generalized contraction mappings, Pacific J. Math. 38 (1971), 89-94. MR 0305160 (46:4290)
  • [7] -, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339-346. MR 0346605 (49:11330)
  • [8] T.-C. Lim, Characterization of normal structure, Proc. Amer. Math. Soc. 43 (1974), 313-319. MR 0361728 (50:14173)
  • [9] -, A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space, Bull. Amer. Math. Soc. 80 (1974), 1123-1126. MR 0394333 (52:15136)
  • [10] -, The asymptotic center and fixed point theorems for nonexpansive mappings, Ph.D. Thesis, Dalhousie Univ., 1974.
  • [11] Z. Opial, Lecture notes on nonexpansive and monotone mappings in Banach spaces, Center for Dynamical Systems, Brown Univ., Providence, R. I., 1967.

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DOI: https://doi.org/10.1090/S0002-9939-1977-0473935-9
Article copyright: © Copyright 1977 American Mathematical Society

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