On a problem of A. Lupaş.
On a Problem of H. Berens.
On a problem of Turán: (0, 2) quadrature formula with a high algebraic degree of precision.
On a Problem Proposed by H. Braß Concerning the Remainder Term in Quadrature for Convex Functions.
On a q-analogue of Stancu operators
This paper is concerned with a generalization in q-Calculus of Stancu operators. Involving modulus of continuity and Lipschitz type maximal function, we give estimates for the rate of convergence. A probabilistic approach is presented and approximation properties are established.
On a sequence of linear and positive operators.
On a subclass of functions for which the Lagrange interpolation yields the Jackson order of approximation.
On a Tauberian theorem of Keldysh.
On a Theorem of Ingham.
On a theorem which limits the number of mixed interpolated derivatives for some plane regular uniform rectangular Birkhoff interpolation schemes.
On algorithms for parabolic splines
On an approximation of function and its derivatives.
On an approximation processes in the space of analytical functions
In this paper we obtain various approximation theorems by means of k-positive linear operators defined on the space of all analytic functions on a bounded domain of the complex plane.
On an expansion theorem in the finite operator calculus of G.-C. Rota.
On an Extremal Problem concerning Bernstein Operators
* The second author is supported by the Alexander-von-Humboldt Foundation. He is on leave from: Institute of Mathematics, Academia Sinica, Beijing 100080, People’s Republic of China.The best constant problem for Bernstein operators with respect to the second modulus of smoothness is considered. We show that for any 1/2 ≤ a < 1, there is an N(a) ∈ N such that for n ≥ N(a), 1−a≤k, n≤a, sup | Bn (f, k/n) − f(k/n) | ≤ cω2(f, 1/√n), where c is a constant,0 < c < 1.
On an Interpolation Process of Lagrange-Hermite Type
On an orthonormal polynomial basis in the space C[-1,1]
We show that in the space C[-1,1] there exists an orthogonal algebraic polynomial basis with optimal growth of degrees of the polynomials.
On Appel-type quadrature rules.
On approximation by Chebyshevian box splines
Chebyshevian box splines were introduced in [5]. The purpose of this paper is to show some new properties of them in the case when the weight functions are of the form , where the functions are periodic functions of one variable. Then we consider the problem of approximation of continuous functions by Chebyshevian box splines.
On approximation by Lagrange interpolating polynomials for a subset of the space of continuous functions
We construct a piecewise differentiable function that is not piecewise analytic and satisfies a Jackson type estimate for approximation by Lagrange interpolating polynomials associated with the extremal points of the Chebyshev polynomials.