Parametric generalization of the modified Bernstein operators

On the approximation by Chlodowsky type generalization of (p,q)-Bernstein operators

In the present article, we introduce Chlodowsky variant of $(p,q)$-Bernstein operators and compute the moments for these operators which are used in proving our main results. Further, we study some approximation properties of these new operators, which include the rate of convergence using usual modulus of continuity and also the rate of convergence when the function $f$ belongs to the class Li...

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 Dunkl generalization of q-parametric Szász-Mirakjan operators

In this paper, we construct a linear positive operators q-parametric Szász Mirakjan operators generated by the q-Dunkl generalization of the exponential function. We obtain Korovkin’s type approximation theorem for these operators and compute convergence of these operators by using the modulus of continuity. Furthermore, the rate of convergence of the operators for functions belonging to the Li...