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Lim, Teck-Cheong

A fixed point theorem for multivalued nonexpansive mappings in a uniformly convex Banach space. (English) Zbl 0297.47045

Bull. Am. Math. Soc. 80, 1123-1126 (1974).
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Cited in 107 Documents

MSC:

47H10 Fixed-point theorems
54C60 Set-valued maps in general topology
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\textit{T.-C. Lim}, Bull. Am. Math. Soc. 80, 1123--1126 (1974; Zbl 0297.47045)
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References:

[1] Nadim A. Assad and W. A. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific J. Math. 43 (1972), 553 – 562. · Zbl 0239.54032
[2] Felix E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces, Nonlinear functional analysis (Proc. Sympos. Pure Math., Vol. XVIII, Part 2, Chicago, Ill., 1968) Amer. Math. Soc., Providence, R. I., 1976, pp. 1 – 308.
[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. · Zbl 0215.48202
[4] Michael Edelstein, The construction of an asymptotic center with a fixed-point property, Bull. Amer. Math. Soc. 78 (1972), 206 – 208. · Zbl 0231.47029
[5] Michael Edelstein, Fixed point theorems in uniformly convex Banach spaces, Proc. Amer. Math. Soc. 44 (1974), 369 – 374. · Zbl 0286.47035
[6] A. L. Garkavi, On the optimal net and best cross-section of a set in a normed space, Izv. Akad. Nauk SSSR Ser. Mat. 26 (1962), 87 – 106 (Russian). · Zbl 0108.10801
[7] E. Lami Dozo, Multivalued nonexpansive mappings and Opial’s condition, Proc. Amer. Math. Soc. 38 (1973), 286 – 292. · Zbl 0268.47060
[8] Teck Cheong Lim, A fixed point theorem for families on nonexpansive mappings, Pacific J. Math. 53 (1974), 487 – 493. · Zbl 0291.47032
[9] Teck Cheong Lim, Characterizations of normal structure, Proc. Amer. Math. Soc. 43 (1974), 313 – 319. · Zbl 0284.47031
[10] T. C. Lim, On asymptotic center and its applications to fixed point theory (submitted).
[11] Jack T. Markin, A fixed point theorem for set valued mappings, Bull. Amer. Math. Soc. 74 (1968), 639 – 640. · Zbl 0159.19903
[12] Sam B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475 – 488. · Zbl 0187.45002
[13] Wacław Sierpiński, Cardinal and ordinal numbers, Second revised edition. Monografie Matematyczne, Vol. 34, Państowe Wydawnictwo Naukowe, Warsaw, 1965. · Zbl 0131.24801
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