On a hybrid family of summation integral type operators.
On a new type of Meyer-Konig and Zeller operators.
On approximation of integrable functions by modified Bernstein polynomials.
On convergence of orthogonal series of Bessel functions
On convex Bézier triangles
On exponential approximation
On maximal inequalities arising in best approximation.
On Müntz rational approximation in multivariables
The present paper shows that for any sequences of real numbers, each with infinitely many distinct elements, , j=1,...,s, the rational combinations of are always dense in .
On regularization in superreflexive Banach spaces by infimal convolution formulas
We present here a new method for approximating functions defined on superreflexive Banach spaces by differentiable functions with α-Hölder derivatives (for some 0 < α≤ 1). The smooth approximation is given by means of an explicit formula enjoying good properties from the minimization point of view. For instance, for any function f which is bounded below and uniformly continuous on bounded sets this formula gives a sequence of Δ-convex functions converging to f uniformly on bounded sets and...
On Representations of Algebraic Polynomials by Superpositions of Plane Waves
* The author was supported by NSF Grant No. DMS 9706883.Let P be a bi-variate algebraic polynomial of degree n with the real senior part, and Y = {yj }1,n an n-element collection of pairwise noncolinear unit vectors on the real plane. It is proved that there exists a rigid rotation Y^φ of Y by an angle φ = φ(P, Y ) ∈ [0, π/n] such that P equals the sum of n plane wave polynomials, that propagate in the directions ∈ Y^φ .
On simultaneous approximation for certain Baskakov Durrmeyer type operators.
On the approximate values of an implicitly given function
On the approximation by compositions of fixed multivariate functions with univariate functions
The approximation in the uniform norm of a continuous function f(x) = f(x₁,...,xₙ) by continuous sums g₁(h₁(x)) + g₂(h₂(x)), where the functions h₁ and h₂ are fixed, is considered. A Chebyshev type criterion for best approximation is established in terms of paths with respect to the functions h₁ and h₂.
On the best approximation properties of -smooth functions on an interval of the real axis (to the phenomenon of unsaturated numerical methods).
On the density of the dilations and translates of function in
On the impossibility of approximating convex functions with ones.
On the lower semi-continuity of the set valued metric projection.
On the Number of Best Approximations in Certain Non-Linear Families of Functions. (Short Communication).
On the rate of approximation for the Bézier variant of Kantorovich-Balazs operators.
On the rate of convergence for modified Szász-Mirakyan operators on functions of bounded variation.