On error estimates for interpolating splines with minimal defect
On estimates for the moduli of smoothness of functions with a transformed Fourier series.
On global approximation properties of abstract integral operators in Orlicz spaces and applications.
On global smoothness preservation in complex approximation
By using the properties of convergence and global smoothness preservation of multivariate Weierstrass singular integrals, we establish multivariate complex Carleman type approximation results with rates. Here the approximants fulfill the global smoothness preservation property. Furthermore Mergelyan's theorem for the unit disc is strengthened by proving the global smoothness preservation property.
On Hermite interpolation formula.
On integral Bernstein operators in some classes of measurable bivariate functions.
On Kantorovich-type operator.
On Korovkin type theorem in the space of locally integrable functions
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space does not hold in all this space and is satisfied only on some subspace.
On Nonlinear Condensation Principles with Rates.
On Projection Constants of Polynomial Spaces on the Unit Ball in Several Variables.
On q-Szász-Durrmeyer operators
In the present paper, we introduce the q-Szász-Durrmeyer operators and justify a local approximation result for continuous functions in terms of moduli of continuity. We also discuss a Voronovskaya type result for the q-Szász-Durrmeyer operators.
On some constants in approximation by Bernstein operators.
On some generalization of box splines
We give a generalization of box splines. We prove some of their properties and we give applications to interpolation and approximation of functions.
On some properties of the Picard operators
We consider the Picard operators and in exponential weighted spaces. We give some elementary and approximation properties of these operators.
On some regular and singular problems of Birkhoff interpolation.
On some shift invariant integral operators, univariate case
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...
On superadditive rates of convergence
On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions
AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined Kfunctional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such...
On the approximation of continuous functions.
On the approximation of functions by matrix means in the generalized Hölder metric
Under some assumptions on the matrix of a summability method, whose rows are sequences of bounded variation, we obtain a generalization and an improvement of some results of Xie-Hua Sun and L. Leindler.