We prove an identity for basis functions of a general family of positive linear operators. It covers as special cases the Bernstein, Szász–Mirakjan and Baskakov operators. A corollary of our result can be considered a pointwise orthogonality relation. The Bernstein case is the univariate case of a remarkable identity which recently was presented by Jetter and Stöckler. As an application we give...

In this study, we have constructed a sequence of new positive linear operators with two variable by using Szasz-Mirakyan and Bernstein Operators, and investigated its approximation properties.

In the present paper, we introduce a kind of Durrmeyer variant of Bernstein-Stancu operators, and we obtain the direct and converse results of approximation by the operators.

Approximation properties of Bernstein operators have been studied very well (see [2], [3], [5]-[8], [12]-[14], for example). In order to approximate the functions with singularities, Della Vecchia et al. [3] and Yu-Zhao [12] introduced some kinds of modified Bernstein operators. Throughout the paper, C denotes a positive constant independent of n and x, which may be different in different cases...

Bǎrbosu and Muraru (2015) introduced the bivariate generalization of the q -Bernstein–Schurer–Stancu operators and constructed a GBS operator of q -Bernstein–Schurer–Stancu type. The concern of this paper is to obtain the rate of convergence in terms of the partial and complete modulus of continuity and the degree of approximation by means of Lipschitz-type class for the bivariate operators. In...

In this study, we introduce a new kind of nonlinear Bernstein-Chlodowsky operators based on q-integers. Firstly, define the q?Bernstein-Chlodowsky max-product kind. Then, give an error estimation for q?Bernstein Chlodowsky by using suitable generalizition Shisha-Mond Theorem. There follows upper estimates approximation some subclasses functions.

Replacing the nested sequence of ""nite" dimensional subspaces by the nested sequence of "closed" subspaces in the classical Bernstein lethargy theorem, we obtain a version of this theorem for the space B(X; Y) of all bounded linear maps. Using this result and some properties of diagonal operators, we investigate conditions under which a suitable pair of Banach spaces form an exact Bernstein pa...