There exists a surface of a convex polyhedron P and a partition L of P into geodesic convex polygons such that there are no connected"edge"unfoldings of P without self-intersections (whose spanning tree is a subset of the edge skeleton of L).

In this paper, mainly using the convexity of the function a −b cx−dx and convexity or concavity of the function ln a −b cx−dx on the real line, where a > b ≥ c > d > 0 are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements. 2000 Mathematics Subject C...

It is shown that a subset of a uniformly convex normed space is nearly convex if and only if its closure is convex. Also, a normed space satisfying a mild completeness property is strictly convex if and only if every metrically convex subset is convex. 1 Classical and constructive mathematics The arguments in this paper conform to constructive mathematics in the sense of Errett Bishop. This mea...

Let f ∈ C[−1, 1] change its convexity finitely many times, in the interval. We are interested in estimating the degree of approximation of f by polynomials, and by piecewise polynomials, which are coconvex with it, namely, polynomials and piecewise polynomials that change their convexity exactly at the points where f does. We obtain Jackson type estimates and summarize the positive and negative...

We introduce the notions of pointwise modulus of squareness and local modulus of squareness of a normed space X. This answers a question of C. Benitez, K. PrzesÃlawski and D. Yost about the definition of a sensible localization of the modulus of squareness. Geometrical properties of the norm of X (Fréchet smoothness, Gâteaux smoothness, local uniform convexity or strict convexity) are character...

In this paper, mainly using the convexity of the function a x −b x cx−dx and convexity or concavity of the function ln a x −b x cx−dx on the real line, where a > b ≥ c > d > 0 are fixed real numbers, we obtain some important relations between various important means of these numbers. Also, we apply the obtained results to Ky Fan type inequalities and get some new refinements. 2000 Mathematics S...

Let S be a subset of R with finite positive Lebesgue measure. The Beer index of convexity b(S) of S is the probability that two points of S chosen uniformly independently at random see each other in S. The convexity ratio c(S) of S is the Lebesgue measure of the largest convex subset of S divided by the Lebesgue measure of S. We investigate the relationship between these two natural measures of...

G. Murugusundaramoorthy, S. Sivasubramanian, R. K. Raina Abstract. The authors introduce a new subclass UH(α, β, γ, δ, λ, k) of functions which are analytic in the open disc ∆ = {z ∈ C : |z| < 1}. Various results studied include the coefficient estimates and distortion bounds, radii of close-to-convexity, starlikeness and convexity and integral means inequalities for functions belonging to the ...

Gordon G Johnson* ([email protected]), Department of Mathematics, University of Houston, Houston, TX 77204-3008. The Closure in a Hilbert Space of a PreHilbert Space CHEBYSHEV Set Fails to be a CHEBYSHEV Set. Preliminary report. E is the real inner product space that is union of all finite-dimensional Euclidean spaces, S is a certain bounded nonconvex set in the E having the property that every...

We show that a PL-realization of a closed connected manifold of dimension n − 1 in R (n ≥ 3) is the boundary of a convex polyhedron if and only if the interior of each (n− 3)-face has a point, which has a neighborhood lying on the boundary of a convex n-dimensional body. This result is derived from a generalization of Van Heijenoort’s theorem on locally convex manifolds to the spherical case. O...