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Kirk, W. A.

Fixed point theorems for non-Lipschitzian mappings of asymptotically nonexpansive type. (English) Zbl 0286.47034

Isr. J. Math. 17, 339-346 (1974).
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Cited in 96 Documents

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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\textit{W. A. Kirk}, Isr. J. Math. 17, 339--346 (1974; Zbl 0286.47034)
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References:

[1] Browder, F. E., Nonexpansive nonlinear operators in a Banach space, Proc. Nat. Acad. Sci. U. S. A., 54, 1041-1044 (1965) · Zbl 0128.35801 · doi:10.1073/pnas.54.4.1041
[2] Clarkson, J. A., Uniformly convex spaces, Trans. Amer. Math. Soc., 40, 396-414 (1936) · Zbl 0015.35604 · doi:10.2307/1989630
[3] De Marr, R., Common fixed points for commuting contraction mappings, Pacific J. Math., 13, 1139-1141 (1963) · Zbl 0191.14901
[4] Goebel, K., Convexity of balls and fixed-point theorems for mappings with nonexpansive square, Compositio Math., 22, 269-274 (1970) · Zbl 0202.12802
[5] Goebel, K.; Kirk, W. A., A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35, 171-174 (1972) · Zbl 0256.47045 · doi:10.2307/2038462
[6] Goebel, K.; Kirk, W. A., A fixed point theorem for mappings whose iterates have uniform Lipschitz constant, Studia Math., 47, 135-140 (1973) · Zbl 0265.47044
[7] K. Goebel, W. A. Kirk, and R. L. Thele,Uniformly Lipschitzian families of transformations in Banach spaces (to appar). · Zbl 0275.47041
[8] Göhde, D., Zum prinzip der kontraktiven Abbildung, Math. Nachr., 30, 251-258 (1965) · Zbl 0127.08005 · doi:10.1002/mana.19650300312
[9] Gurarii, V. I., On the differential properties of the modulus of convexity in a Banach space, Mat. Issled., 2, 141-148 (1967) · Zbl 0232.46024
[10] James, R. C., Uniformly non-square Banach spaces, Ann. of Math., 80, 542-550 (1964) · Zbl 0132.08902 · doi:10.2307/1970663
[11] Kirk, W. A., A fixed point theorem for mappings which do not increases distances, Amer. Math. Monthly, 72, 1004-1006 (1965) · Zbl 0141.32402 · doi:10.2307/2313345
[12] Milman, Ju. I., Geometric theory of Banach spaces II, Geometry of the unit ball, Uspehi Mat. Nauk, 26, 73-150 (1971)
[13] Opial, Z., Lecture notes on nonexpansive and monotone mappings in Banach spaces (1967), Providence, R. I.: Center for Dynamical Systems, Brown University, Providence, R. I. · Zbl 0179.19902
[14] Schaefer, H., Über die Methode sukzessiver Approximationen, Jber, Deutsch. Math.-Verein, 59, 131-140 (1957) · Zbl 0077.11002
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