On local and global moduli of convexity
On local convexity of nonlinear mappings between Banach spaces
We find conditions for a smooth nonlinear map f: U → V between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some c and each positive ɛ < c the image f(B ɛ(x)) of each ɛ-ball B ɛ(x) ⊂ U is convex. We give a lower bound on c via the second order Lipschitz constant Lip2(f), the Lipschitz-open constant Lipo(f) of f, and the 2-convexity number conv2(X) of the Banach space X.
On mappings preserving a family of star bodies.
On maximal ot-subsets of the Euclidean plane.
On minimum area quadrilaterals and triangles circumscribed about convex plane regions.
On minimum kissing numbers of finite translative packings of a convex body.
On monotone minimal cuscos
On Multiple Space Subdivisions by Zonotopes.
On Nash theorem
On new isoperimetric inequalities and symmetrization.
On non-inscribable polytopes
On optimal route planning evading cubes in the three space.
On order and metric convexities in
On parametric density of finite circle packings.
On periodic homeomorphisms of spheres.
On point classification in convex sets.
On point sets fixing a convex body from within.
On prior distributions which give rise to a dominated Bayesian experiment.
On properties of geodesic -preinvex functions.
On reduced pairs of bounded closed convex sets.
In this paper certain criteria for reduced pairs of bounded closed convex set are presented. Some examples of reduced and not reduced pairs are enclosed.