In this note we present a new characterization of Bernstein operators by showing that they are the only solution of a certain extremal relation. © 2006 Elsevier Inc. All rights reserved.

In this paper, we introduce a new type λ-Bernstein operators with parameter [Formula: see text], we investigate a Korovkin type approximation theorem, establish a local approximation theorem, give a convergence theorem for the Lipschitz continuous functions, we also obtain a Voronovskaja-type asymptotic formula. Finally, we give some graphs and numerical examples to show the convergence of [For...

New modified Schurer-type q-Bernstein Kantorovich operators are introduced. The local theorem and statistical Korovkin-type approximation properties of these operators are investigated. Furthermore, the rate of approximation is examined in terms of the modulus of continuity and the elements of Lipschitz class functions.

Our main purpose of this article is to study the convergence and other related properties q-Bernstein-Kantorovich operators including shifted knots real positive numbers. We design Bernstein-Kantorovich generated by basic q-calculus. More precisely, we our new in space continuous functions Lebesgue space. obtain degree with help modulus continuity integral continuity. Furthermore, establish qua...

The objective of this paper is to give some probabilistic derivations the Cheney, Sharma, and Bernstein approximation operators. Motivated by these derivations, generalizations operators are defined. convergence property generalization established. It also shown that Cheney–Sharma operator Szász–Mirakyan averaged a certain probability distribution.

"In this paper, we consider the complex form of a new generalization Bernstein-Schurer operators. We obtain some quantitative upper estimates for approximation these operators attached to analytic functions. Moreover, prove that preserve properties original function such as univalence, starlikeness, convexity and spirallikeness."