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Caristi, James

Fixed point theorems for mappings satisfying inwardness conditions. (English) Zbl 0305.47029

Trans. Am. Math. Soc. 215, 241-251 (1976).
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Cited in 57 Reviews
Cited in 357 Documents

MSC:

47H10 Fixed-point theorems
54H25 Fixed-point and coincidence theorems (topological aspects)
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References:

[1] Haïm Brezis, On a characterization of flow-invariant sets, Comm. Pure Appl. Math. 23 (1970), 261 – 263. · Zbl 0191.38703 · doi:10.1002/cpa.3160230211
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[3] Felix E. Browder, The fixed point theory of multi-valued mappings in topological vector spaces, Math. Ann. 177 (1968), 283 – 301. · Zbl 0176.45204 · doi:10.1007/BF01350721
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[10] Tosio Kato, Nonlinear semigroups and evolution equations, J. Math. Soc. Japan 19 (1967), 508 – 520. · Zbl 0163.38303 · doi:10.2969/jmsj/01940508
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[12] W. A. Kirk, Fixed point theorems for nonexpansive mappings satisfying certain boundary conditions, Proc. Amer. Math. Soc. 50 (1975), 143 – 149. · Zbl 0322.47036
[13] R. H. Martin Jr., Differential equations on closed subsets of a Banach space, Trans. Amer. Math. Soc. 179 (1973), 399 – 414. · Zbl 0293.34092
[14] W. V. Petryshyn and P. M. Fitzpatrick, Fixed point theorems for multivalued non-compact inward maps (to appear). · Zbl 0287.47038
[15] R. M. Redheffer, The theorems of Bony and Brezis on flow-invariant sets, Amer. Math. Monthly 79 (1972), 740 – 747. · Zbl 0278.34039 · doi:10.2307/2316263
[16] Simeon Reich, Fixed points in locally convex spaces, Math. Z. 125 (1972), 17 – 31. · Zbl 0216.17302 · doi:10.1007/BF01111112
[17] Simeon Reich, Remarks on fixed points, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur. (8) 52 (1972), 689 – 697 (English, with Italian summary). · Zbl 0256.47043
[18] Simeon Reich, Fixed points of condensing functions, J. Math. Anal. Appl. 41 (1973), 460 – 467. · Zbl 0252.47062 · doi:10.1016/0022-247X(73)90220-5
[19] Simeon Reich, Fixed points of non-expansive functions, J. London Math. Soc. (2) 7 (1973), 5 – 10. · Zbl 0268.47058 · doi:10.1112/jlms/s2-7.1.5
[20] G. Vidossich, Existence comparison and asymptotic behavior of solutions of ordinary differential equations in finite and infinite dimensional Banach spaces (to appear).
[21] -, Nonexistence of periodic solutions of differential equations and applications to zeros of nonlinear operators (to appear).
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