The aim of this paper is to construct a class of linear operators in more general conditions. The method was inspired by Jakimovski and Leviatan (see [1]). We do not study the convergence of these operators with the well-known theorem of Bohman-Korovkin. The evaluation theorems for the rate of convergence are different from the well-known theorem of Shisha-Mond. We prove the Voronovskaja-type t...

We prove a multivariate Whitney type theorem for the local anisotropic polynomial approximation in Lp(Q) with 1 ≤ p ≤ ∞. Here Q is a d-parallelepiped in R with sides parallel to the coordinate axes. We consider the error of best approximation of a function f by algebraic polynomials of fixed degree at most ri− 1 in variable xi, i = 1, ..., d, and relate it to a so-called total mixed modulus of ...

In this paper, using the best proximity theorems for an extensionof Brosowski's theorem. We obtain other results on farthest points. Finally, wedene the concept of e- farthest points. We shall prove interesting relationshipbetween the -best approximation and the e-farthest points in normed linearspaces (X; ||.||). If z in W is a e-farthest point from an x in X, then z is also a-best approximati...

The current paper deals with the parametric modification of Bernstein operators which preserve constant and Korovkin?s other test functions in limit case. uniform convergence newly constructed is studied. Also, rate investigated by means modulus continuity, using belong to Lipschitz class help Peetre?s-K functionals. Finally, some numerical examples are given illustrate effectiveness defined fo...

In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absol...

We provide a version of Korovkin-type theorems for monotone sublinear operators in vector lattices
 and discuss the possibilities further extensions generalizations. 
 .

In this paper we will demonstrate a Voronovskaja-type theorem and approximation theorem for GBS operator associated to a linear positive operator.