A generalization of Altman’s ordering principle

Turinici, Mihai

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

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
Full-text PDF Free Access

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] Mieczyslaw Altman, Contractors and contractor directions. Theory and applications, Marcel Dekker, Inc., New York-Basel, 1977. A new approach to solving equations; Lecture Notes in Pure and Applied Mathematics, Vol. 32. MR 0451686
[2] Mieczyslaw Altman, An existence principle in nonlinear functional analysis, Nonlinear Anal. 2 (1978), no. 6, 765–771. MR 512166, https://doi.org/10.1016/0362-546X(78)90018-4
[3] Mieczyslaw Altman, A generalization of the Brézis-Browder principle on ordered sets, Nonlinear Anal. 6 (1982), no. 2, 157–165. MR 651697, https://doi.org/10.1016/0362-546X(82)90084-0
[4] 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 0425688, https://doi.org/10.1016/S0001-8708(76)80004-7
[5] W. J. Cramer Jr. and William O. Ray, Solvability of nonlinear operator equations, Pacific J. Math. 95 (1981), no. 1, 37–50. MR 631657
[6] Ivar Ekeland, Nonconvex minimization problems, Bull. Amer. Math. Soc. (N.S.) 1 (1979), no. 3, 443–474. MR 526967, https://doi.org/10.1090/S0273-0979-1979-14595-6
[7] Mihai Turinici, A generalization of Brézis-Browder’s ordering principle, An. Ştiinţ. Univ. “Al. I. Cuza” Iaşi Secţ. I a Mat. (N.S.) 28 (1982), no. 1, 11–16. MR 667714
[8] Mihai Turinici, Constant and variable drop theorems on metrizable locally convex spaces, Comment. Math. Univ. Carolin. 23 (1982), no. 2, 383–398. MR 664983
[9] 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