Results 11 to 20 of about 330 (59)
ANY CYCLIC QUADRILATERAL CAN BE INSCRIBED IN ANY CLOSED CONVEX SMOOTH CURVE
Forum of Mathematics, Sigma, 2018 We prove that any cyclic quadrilateral can be inscribed in any closed convex $C^{1}$ -curve. The smoothness condition is not required if the quadrilateral is a rectangle.
ARSENIY AKOPYAN, SERGEY AVVAKUMOV
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
On multiplicity of mappings between surfaces [PDF]
, 2008 Let M and N be two closed (not necessarily orientable) surfaces, and f a continuous map from M to N. By definition, the minimal multiplicity MMR[f] of the map f denotes the minimal integer k having the following property: f can be deformed into a map g ...
Bogatyi, Semeon +2 more
core +3 more sources
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
Extensions of best approximation and coincidence theorems
International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 4, Page 689-698, 1997., 1997 Let X be a Hausdorff compact space, E a topological vector space on which E* separates points, F : X → 2E an upper semicontinuous multifunction with compact acyclic values, and g : X → E a continuous function such that g(X) is convex and g−1(y) is acyclic for each y ∈ g(X).
Sehie Park
wiley +1 more source
On Fox spaces and Jacobi identities [PDF]
, 2007 In 1945, R. Fox introduced the so-called Fox torus homotopy groups in which the usual homotopy groups are embedded and their Whitehead products are expressed as commutators.
Golasinski, Marek +2 more
core +3 more sources
Bourgin-Yang versions of the Borsuk-Ulam theorem for $p$-toral groups [PDF]
, 2016 Let $V$ and $W$ be orthogonal representations of $G$ with $V^G= W^G=\{0\}$. Let $S(V )$ be the sphere of $V$ and $f : S(V ) \to W$ be a $G$-equivariant mapping. We give an estimate for the dimension of the set $Z_f=f^{-1}\{0\}$ in terms of $ \dim V$ and $
de Mattos, Denise +2 more
core +1 more source
Topological methods in zero-sum Ramsey theory
Forum of Mathematics, SigmaA landmark result of Erdős, Ginzburg, and Ziv (EGZ) states that any sequence of $2n-1$ elements in ${\mathbb {Z}}/n$ contains a zero-sum subsequence of length n.
Florian Frick +7 more
doaj +1 more source
Maps on graphs can be deformed to be coincidence-free [PDF]
, 2010 We give a construction to remove coincidence points of continuous maps on graphs (1-complexes) by changing the maps by homotopies. When the codomain is not homeomorphic to the circle, we show that any pair of maps can be changed by homotopies to be ...
Staecker, P. Christopher
core +2 more sources
Twisted Burnside-Frobenius theory for endomorphisms of polycyclic groups
, 2017 Let $R(\phi)$ be the number of $\phi$-conjugacy (or Reidemeister) classes of an endomorphism $\phi$ of a group $G$. We prove for several classes of groups (including polycyclic) that the number $R(\phi)$ is equal to the number of fixed points of the ...
Fel'shtyn, Alexander, Troitsky, Evgenij
core +1 more source