A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space

Author:
Teck-Cheong Lim

Journal:
Bull. Amer. Math. Soc. **80** (1974), 1123-1126

MSC (1970):
Primary 46A05

DOI:
https://doi.org/10.1090/S0002-9904-1974-13640-2

MathSciNet review:
0394333

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References | Similar Articles | Additional Information

**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**341459****2.**F. E. Browder,*Nonlinear operators and nonlinear equations of evolution in Banach spaces*, Proc. Sympos. Pure Math., vol. 18, part II, Amer. Math. Soc., Providence, R.I. (to appear). MR**405188****3.**M. M. Day, R. C James and S. Swaminathan,*Normed linear spaces that are uniformly convex in every direction*, Canad. J. Math. 23 (1971), 1051-1059. MR 44 #4492. MR**287285****4.**M. Edelstein,*The construction of an asymptotic center with a fixed point property*, Bull. Amer. Math. Soc. 78 (1972), 206-208. MR 45 #1005. MR**291917****5.**M. Edelstein,*Fixed point theorems in uniformly convex Banach spaces*(to appear). MR**358451****6.**A. L. Garkavi,*The best possible net and the best possible cross-section of a set in a normed space*, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87-106; English transl., Amer. Math. Soc. Transl. (2) 39 (1964), 111-132. MR 25 #429. MR**136969****7.**E. Lami Dozo,*Multivalued nonexpansive mappings and Opial's condition*, Proc. Amer. Math. Soc. 38 (1973), 286-292. MR 46 #9816. MR**310718****8.**T. C. Lim,*A fixed point theorem for families of nonexpansive mappings*, Pacific J. Math. (to appear). MR**365250****9.**T. C. Lim,*Characterizations of normal structure*, Proc. Amer. Math. Soc. 43 (1974), 313-319. MR**361728****10.**T. C. Lim,*On asymptotic center and its applications to fixed point theory*(submitted).**11.**J. T. Markin,*A fixed point theorem for set valued mappings*, Bull. Amer. Math. Soc. 74 (1968), 639-640. MR 37 #3409. MR**227825****12.**S. B. Nadler, Jr.,*Multi-valued contraction mappings*, Pacific J. Math. 30 (1969), 475-488. MR 40 #8035. MR**254828****13.**W. Sierpiński,*Cardinal and ordinal numbers*, 2nd rev. ed., Monografie Mat., vol. 34, PWN, Warsaw, 1965, p. 382 and p. 390. MR 33 #2549. MR**194339**

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DOI:
https://doi.org/10.1090/S0002-9904-1974-13640-2