A generalization of Altman’s ordering principle

Turinici, Mihai

doi:10.1090/S0002-9939-1984-0722430-1

A generalization of Altman’s ordering principle
HTML articles powered by AMS MathViewer

by Mihai Turinici

Proc. Amer. Math. Soc. 90 (1984), 128-132

DOI: https://doi.org/10.1090/S0002-9939-1984-0722430-1

PDF | Request permission

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.

References

Mieczyslaw Altman, Contractors and contractor directions. Theory and applications, Lecture Notes in Pure and Applied Mathematics, Vol. 32, Marcel Dekker, Inc., New York-Basel, 1977. A new approach to solving equations. MR 0451686
Mieczyslaw Altman, An existence principle in nonlinear functional analysis, Nonlinear Anal. 2 (1978), no. 6, 765–771. MR 512166, DOI 10.1016/0362-546X(78)90018-4
Mieczyslaw Altman, A generalization of the Brézis-Browder principle on ordered sets, Nonlinear Anal. 6 (1982), no. 2, 157–165. MR 651697, DOI 10.1016/0362-546X(82)90084-0
H. Brézis and F. E. Browder, A general principle on ordered sets in nonlinear functional analysis, Advances in Math. 21 (1976), no. 3, 355–364. MR 425688, DOI 10.1016/S0001-8708(76)80004-7
W. J. Cramer Jr. and William O. Ray, Solvability of nonlinear operator equations, Pacific J. Math. 95 (1981), no. 1, 37–50. MR 631657, DOI 10.2140/pjm.1981.95.37
Ivar Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 3, 443–474. MR 526967, DOI 10.1090/S0273-0979-1979-14595-6
Mihai Turinici, A generalization of Brézis-Browder’s ordering principle, An. Şti. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 28 (1982), no. 1, 11–16. MR 667714
Mihai Turinici, Constant and variable drop theorems on metrizable locally convex spaces, Comment. Math. Univ. Carolin. 23 (1982), no. 2, 383–398. MR 664983
Mihai Turinici, Mapping theorems via contractor directions in metrizable locally convex spaces, Bull. Acad. Polon. Sci. Sér. Sci. Math. 30 (1982), no. 3-4, 161–166 (English, with Russian summary). MR 673440