A New Class of Modified Bernstein Operators

Bernstein-Schnabl operators: new achievements and perspectives

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...

Statistical approximation of modified Schurer-type q-Bernstein Kantorovich operators

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.

On simultaneous approximation for some modified Bernstein-type operators

for n ≥ α, where α, β are integers satisfying α ≥ β ≥ 0 and In ⊆ {0,1,2, . . . ,n} is a certain index set. For α = β = 0, In = {0}, this definition reduces to the BernsteinDurrmeyer operators, which were first studied by Derriennic [3]. Also if α = β = 1, In = {0}, we obtain the recently introduced sequence of Gupta and Maheshwari [4], that is, Mn,1,1(f ,x)≡ Pn(f ,x) which is defined as Pn(f ,x...

Modified (p,q)-Bernstein-Schurer operators and their approximation properties

A new estimate for Hölder approximation by Bernstein operators

In this work we discuss the rate of simultaneous approximation of Hölder continuous functions by Bernstein operators, measured by Hölder norms with different exponents. We extend the known results on this topic.