In the present paper, we introduce a new variant of Bernstein-Kantorovich operators which reproduce affine functions. The approximation rate for continuous functions and Voronovskaja?s asymptotic estimate are obtained.

In the present paper a Korovkin-type theorem is proposed for the approximation operators defined by the inverse Ftransforms. These results allow us to choose between a variety of shapes to be used as atoms of the fuzzy partitions used within the F-transform’s framework. In this way we can enlarge considerably the class of F-transforms proposed recently by I. Perfilieva. The new fuzzy partitions...

Purpose: The purpose of this paper is to introduce the mixed summation-integral-type Lupaş-Phillips-Bernstein operators. Methods: Firstly, we compute the moments of the operators. We use the method of Korovkin-type statistical approximation and modulus of continuity. Results: We find the rate of convergence of the modified operators using statistical convergence and modulus of continuity. Concl...

This paper investigates the approximation of set-valued functions with compact images (not necessarily convex), by adaptations of the Schoenberg spline operators and the Bernstein polynomial operators. When replacing the sum between numbers in these operators, by the Minkowski sum between sets, the resulting operators approximate only set valued functions with compact-convex images [10]. To obt...

Bernstein-Schnabl operators were first introduced by R. Schnabl in 1968 in the context of the sets of all probability Radon measures on compact Hausdorff spaces, in order to present a unitary treatment of the saturation problem for Bernstein operators on the unit interval and on the finite dimensional simplices and hypercubes. These operators were referred to as Bernstein-Schnabl operators in 1...

The Bernstein operator Bn for a simplex in Rd is naturally defined via the Bernstein basis obtained from the barycentric coordinates given by its vertices. Here we consider a generalisation of this basis and the Bernstein operator, which is obtained from generalised barycentric coordinates that are given for more general configurations of points in Rd . We call the associated polynomials a Bern...

The aim in our study is giving a generalization of the two-dimensional (p,q)-Bernstein-Stancu operators particular domain. In addition, by creating some direct results these operators, rate convergence studied Lipschitz type functions and modulus continuity.

We construct Bernstein-type operators on a triangle with one curved side. We study univariate operators, their product and Boolean sum, as well as their interpolation properties, the order of accuracy (degree of exactness, precision set) and the remainder of the corresponding approximation formulas. We also give some illustrative examples. Mathematics Subject Classification (2010). Primary 41A3...

The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...