A generalization of Altman's ordering principle
Author:
Mihai Turinici
Journal:
Proc. Amer. Math. Soc. 90 (1984), 128-132
MSC:
Primary 54F05; Secondary 06A10, 39B70, 54C10
DOI:
https://doi.org/10.1090/S0002-9939-1984-0722430-1
MathSciNet review:
722430
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Abstract | References | Similar Articles | Additional Information
Abstract: A maximality principle on quasi-ordered quasi-metric spaces, containing, in particular, Altman's and the Brézis-Browder ordering principles, is given. As an application, a local mapping theorem extending--from a "functional" viewpoint--a similar one due to Altman, is derived.
- [1] M. Altman, Contractors and contractor directions, Theory and Applications, Marcel Dekker, New York, 1977. MR 0451686 (56:9968)
- [2] -, An existence principle in nonlinear functional analysis, Nonlinear Anal. 2 (1978), 765-771. MR 512166 (80a:47092)
- [3] -, A generalization of the Brézis-Browder principle on ordered sets, Nonlinear Anal. 6 (1982), 157-165. MR 651697 (83j:06005)
- [4] H. Brézis and F. E. Browder, A general principle on ordered sets in nonlinear functional analysis, Adv. in Math. 21 (1976), 355-364. MR 0425688 (54:13641)
- [5] W. J. Cramer and W. O. Ray, Solvability of nonlinear operator equations, Pacific J. Math. 95 (1981), 37-50. MR 631657 (83j:47046)
- [6] I. Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979), 443-474. MR 526967 (80h:49007)
- [7] M. Turinici, A generalization of Brézis-Browder's ordering principle, An. Ştiinţ. Univ. "A1. I. Cuza" Iaşi Seçt. I-a Mat. (N.S.) 28 (1982), 11-16. MR 667714 (83m:54064)
- [8] -, Constant and variable drop theorems on metrizable locally convex spaces, Comment. Math. Univ. Carolinae 23 (1982), 383-398. MR 664983 (84k:47050)
- [9] -, Mapping theorems via contractor directions in metrizable locally convex spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), 161-165. MR 673440 (84k:47051)
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9939-1984-0722430-1
Keywords:
Quasi-ordering,
maximality principle,
mapping theorem
Article copyright:
© Copyright 1984
American Mathematical Society