Fixed point theorems for mappings of nonexpansive type

Lim, Teck-Cheong

doi:10.1090/S0002-9939-1977-0473935-9

Fixed point theorems for mappings of nonexpansive type
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Proc. Amer. Math. Soc. 66 (1977), 69-74 Request permission

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.

References

Nadim A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972), 553–562. MR 341459
Michael Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 44 (1974), 369–374. MR 358451, DOI 10.1090/S0002-9939-1974-0358451-4
K. Goebel and W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 35 (1972), 171–174. MR 298500, DOI 10.1090/S0002-9939-1972-0298500-3
K. Goebel and W. A. Kirk, A fixed point theorem for transformations whose iterates have uniform Lipschitz constant, Studia Math. 47 (1973), 135–140. MR 336468, DOI 10.4064/sm-47-2-134-140
Robert C. James, Uniformly non-square Banach spaces, Ann. of Math. (2) 80 (1964), 542–550. MR 173932, DOI 10.2307/1970663
W. A. Kirk, Fixed point theorems for nonlinear nonexpansive and generalized contraction mappings, Pacific J. Math. 38 (1971), 89–94. MR 305160
W. A. Kirk, Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type, Israel J. Math. 17 (1974), 339–346. MR 346605, DOI 10.1007/BF02757136
Teck Cheong Lim, Characterizations of normal structure, Proc. Amer. Math. Soc. 43 (1974), 313–319. MR 361728, DOI 10.1090/S0002-9939-1974-0361728-X
Teck Cheong Lim, A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space, Bull. Amer. Math. Soc. 80 (1974), 1123–1126. MR 394333, DOI 10.1090/S0002-9904-1974-13640-2

The asymptotic center and fixed point theorems for nonexpansive mappings

Lecture notes on nonexpansive and monotone mappings in Banach spaces