On the Dimension of Bivariate Spline Spaces of Smoothness r and Degree d = 3r + 1.
On the Durrmeyer-type modification of some discrete approximation operators.
On the eigenfunctions of a modified Durrmeyer operator and application.
On the error estimation in numerical methods
On the error of compound quadrature formulas for r-convex functions.
On the Evaluation of Certain Two-Dimensional Singular Integrals with Cauchy Kernels.
On the exact estimates of the best spline approximations of functions.
On the existence and characterization of minimal projections.
On the existence of almost greedy bases in Banach spaces
We consider several greedy conditions for bases in Banach spaces that arise naturally in the study of the Thresholding Greedy Algorithm (TGA). In particular, we continue the study of almost greedy bases begun in [3]. We show that almost greedy bases are essentially optimal for n-term approximation when the TGA is modified to include a Chebyshev approximation. We prove that if a Banach space X has a basis and contains a complemented subspace with a symmetric basis and finite cotype then X has an...
On the Existence of Optimal Integration Formulas for Analytic Functions.
On the expansion of a function in terms of spherical harmonics in arbitrary dimensions.
On the Fast Convergence of a Galerkin-Like Method for Equations of the Second Kind.
On the Fejér means of bounded Ciesielski systems
We investigate the bounded Ciesielski systems, which can be obtained from the spline systems of order (m,k) in the same way as the Walsh system arises from the Haar system. It is shown that the maximal operator of the Fejér means of the Ciesielski-Fourier series is bounded from the Hardy space to if 1/2 < p < ∞ and m ≥ 0, |k| ≤ m + 1. Moreover, it is of weak type (1,1). As a consequence, the Fejér means of the Ciesielski-Fourier series of a function f converges to f a.e. if f ∈ L₁ as n...
On the Fréchet differentiability of distance functions
On the fundamental polynomials for Hermite-Fejér interpolation of Lagrange type on the Chebyshev nodes.
On the gamma and beta approximation operators.
On the generalized Favard-Kantorovich and Favard-Durrmeyer operators in exponential function spaces.
On the impossibility of approximating convex functions with ones.
On The Interpolation Between Certain Theorems On Fourier Transforms.
On the interpolation in linear spaces.