Results 1 to 10 of about 39 (39)
On Hahn-Banach theorem and some of its applications
Open Mathematics, 2022 First, this work provides an overview of some of the Hahn-Banach type theorems. Of note, some of these extension results for linear operators found recent applications to isotonicity of convex operators on a convex cone.
Olteanu Octav
doaj +1 more source
Revisiting Cauty′s proof of the Schauder conjecture
Abstract and Applied Analysis, Volume 2003, Issue 7, Page 407-433, 2003., 2003 The Schauder conjecture that every compact convex subset of a metric linear space has the fixed‐point property was recently established by Cauty (2001). This paper elaborates on Cauty′s proof in order to make it more detailed, and therefore more accessible.
Tadeusz Dobrowolski
wiley +1 more source
Extreme points and support points of conformal mappings
Open Mathematics, 2019 There are three types of results in this paper. The first, extending a representation theorem on a conformal mapping that omits two values of equal modulus. This was due to Brickman and Wilken.
Peretz Ronen
doaj +1 more source
Strongly exposed points in the unit ball of trace‐class operators
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 7, Page 393-397, 2002., 2002 A theorem of Arazy shows that every extreme point of the unit ball of trace‐class operators is strongly exposed. We give this result a simpler and direct proof here.
Kourosh Nourouzi
wiley +1 more source
On boundedly‐convex functions on pseudo‐topological vector spaces
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 141-151, 2000., 2000 Notions of a boundedly convex function and of a Lipschitz‐continuous function are extended to the case of functions on pseudo‐topological vector spaces. It is proved that for “good” pseudo‐topologizers Ψ, any continuous Ψ‐boundedly convex function is Ψ‐differentiable and its derivative is Ψ‐Lipschitz‐continuous.
Vladimir Averbuch
wiley +1 more source
Fixed points, intersection theorems, variational inequalities, and equilibrium theorems
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 2, Page 73-93, 2000., 2000 From a fixed point theorem for compact acyclic maps defined on admissible convex sets in the sense of Klee, we first deduce collectively fixed point theorems, intersection theorems for sets with convex sections, and quasi‐equilibrium theorems. These quasi‐equilibrium theorems are applied to give simple and unified proofs of the known variational ...
Sehie Park
wiley +1 more source
Dynamics of doubly stochastic quadratic operators on a finite-dimensional simplex
Open Mathematics, 2016 The present paper focuses on the dynamics of doubly stochastic quadratic operators (d.s.q.o) on a finite-dimensional simplex. We prove that if a d.s.q.o. has no periodic points then the trajectory of any initial point inside the simplex is convergent. We
Abdulghafor Rawad +3 more
doaj +1 more source
Calculating norms in the spaces l∞(Γ)/c0(Γ) and l∞(Γ)/c(Γ)
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 2, Page 413-415, 1998., 1998 We explicitly compute norms in the quotient spaces l∞(Γ)/c0(Γ) and l∞(Γ)/c(Γ).
Roman Sznajder
wiley +1 more source
Walrasian economy and some properties of convexly compact sets
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 G. Žitković defined the notion of a convexly compact set in a topological space and, among other things, used it to give an extension of the Walrasian excess-demand theorem.
Cristea Mirela +2 more
doaj +1 more source
On the structure of support point sets
International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 1, Page 25-30, 1990., 1990 Let X be a metrizable compact convex subset of a locally convex space. Using Choquet′s Theorem, we determine the structure of the support point set of X when X has countably many extreme points. We also characterize the support points of certain families of analytic functions.
E. Azoff, R. younis
wiley +1 more source