By developing the classical kernel method, Delaigle and Meister provide a nice estimation for a density function with some Fourier-oscillating noises over a Sobolev ballWs 2(L) and over L 2 risk (Delaigle and Meister in Stat. Sin. 21:1065-1092, 2011). The current paper extends their theorem to Besov ball Br,q(L) and L p risk with p,q, r ∈ [1,∞] by using wavelet methods. We firstly show a linear...

Within the categoryW of archimedean lattice-ordered groups with weak order unit, we show that the objects of the form C (L), the set of continuous real-valued functions on a locale L, are precisely those which are divisible and complete with respect to a variant of uniform convergence, here termed indicated uniform convergence. We construct the corresponding completion of aW-object A purely alg...

This paper considers a finite-element approximation of a second-order selfadjoint elliptic equation in a region flcR" (with n = 2 or 3) having a curved boundary dQ on which a Neumann or Robin condition is prescribed. If the finite-element space denned over D, a union of elements, has approximation power h in the L norm, and if the region of integration is approximated by Q* with dist (Q, £?*) =...

Purpose: The purpose of this paper is to introduce and study the BaskakovDurrmeyerStancu operators based on q-integers. Methods: First we use property of q-calculus to estimate moments of these operators. Also study some approximation properties, asymptotic formula including q-derivative and point-wise estimation for the operators L n,q . Results: We studied better error estimations for these o...