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 study the stability of noncompact critica of parametric elliptic functionals with a volume constraint. Let F : U ⊂ S → R be a smooth function. For a smooth, oriented hypersurface X : Σ → E whose Gauss map ν : Σ → S is assumed to lie in U , we define the functional FΛ(X) = ∫ Σ F (ν)dΣ + ΛV (X), Λ ∈ R, (1) where V (X) denotes the algebraic n + 1 dimensional volume enclosed by X, V (X) := 1 n +...

This paper is devoted to introducing a nonlinear reconstruction operator, the piecewise polynomial harmonic (PPH), on nonuniform grids. We define this operator and we study its main properties, such as reproduction of second-degree polynomials, approximation order, conditions for convexity preservation. In particular, σ quasi-uniform grids with σ≤4, get quasi C3 that maintains properties initia...

‎In this paper‎, ‎some properties of pre-monotone operators are proved‎. ‎It is shown that in a reflexive Banach space‎, ‎a full domain multivalued $sigma$-monotone operator with sequentially norm$times$weak$^*$ closed graph is norm$times$weak$^*$ upper semicontinuous‎. ‎The notion of $sigma$-convexity is introduced and the‎ ‎relations between the $sigma$-monotonicity and $sigma$-convexity is i...

in this paper, we study the convexity of the integral operator

In this paper, we mainly discuss the angle modulus of convexity δXa(ϵ) and smoothness ρXa(ϵ) in a real normed linear space X, which are closely related to classical δX(ϵ) ρX(ϵ). Some geometric properties two moduli were investigated. particular, obtained characterization uniform non-squareness terms ρXa(1). Meanwhile, studied relationships between δXa(ϵ), other constants spaces through some equ...