Simultaneous approximation by Lupaş modified operators with weighted function of Szász operators.
Simultaneous approximation by two dimensional hybrid positive linear operators.
Simultaneous approximation for Szász-Mirakian quasi-interpolants
We obtain simultaneous approximation equivalence theorem for Szász-Mirakian quasi-interpolants.
Simultaneous approximation for the Phillips operators.
Some problems regarding Bernstein polynomials.
Some properties of generalized Szàsz type operators of two variables
Some properties of the Schurer type operators.
Some results for modified Bernstein polynomials.
Some results regarding the Bernstein polynomials.
Some theorems of Korovkin type
We take another approach to the well known theorem of Korovkin, in the following situation: X, Y are compact Hausdorff spaces, M is a unital subspace of the Banach space C(X) (respectively, ) of all complex-valued (resp., real-valued) continuous functions on X, S ⊂ M a complex (resp., real) function space on X, ϕₙ a sequence of unital linear contractions from M into C(Y) (resp., ), and a linear isometry from M into C(Y) (resp., ). We show, under the assumption that , where is the Choquet...
Spline Subdivision Schemes for Compact Sets. A Survey
Dedicated to the memory of our colleague Vasil Popov January 14, 1942 – May 31, 1990 * Partially supported by ISF-Center of Excellence, and by The Hermann Minkowski Center for Geometry at Tel Aviv University, IsraelAttempts at extending spline subdivision schemes to operate on compact sets are reviewed. The aim is to develop a procedure for approximating a set-valued function with compact images from a finite set of its samples. This is motivated by the problem of reconstructing a 3D object from...
Stable rank of Fourier algebras and an application to Korovkin theory.
Statistical approximation by positive linear operators
Using A-statistical convergence, we prove a Korovkin type approximation theorem which concerns the problem of approximating a function f by means of a sequence Tₙ(f;x) of positive linear operators acting from a weighted space into a weighted space .
Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers
In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.
Statistical approximation to Bögel-type continuous and periodic functions
In this paper, considering A-statistical convergence instead of Pringsheim’s sense for double sequences, we prove a Korovkin-type approximation theorem for sequences of positive linear operators defined on the space of all real valued Bögel-type continuous and periodic functions on the whole real two-dimensional space. A strong application is also presented. Furthermore, we obtain some rates of A-statistical convergence in our approximation.
Statistical extension of the Korovkin-type approximation theorem.
The Baskakov operators for functions of two variables.
The Convergence and Saturation of Iterations of Positive Linear Operators.
The evaluation of the remainders in approximation formulas by linear positive operators of interpolatory type.
The Lower Estimate for Bernstein Operator
MSC 2010: 41A10, 41A15, 41A25, 41A36For functions belonging to the classes C2[0; 1] and C3[0; 1], we establish the lower estimate with an explicit constant in approximation by Bernstein polynomials in terms of the second order Ditzian-Totik modulus of smoothness. Several applications to some concrete examples of functions are presented.