Abstract
The present paper deals with the limit behavior of iterates of Lupaş q- and (p,q)-Bernstein operators. We obtain the convergence for Lupaş q- and (p,q)-Bernstein operators by using the contraction principle.
Highlights
Introduction and preliminariesFor any f ∈ C[0, 1], the sequence of operators Bn : C[0, 1] → C[0, 1] defined by n Bn(f, x) =n xk(1 – x)n–kf k, x ∈ [0, 1], n ∈ N, k n k=0 (1.1)is known as Bernstein polynomials [6]
Our aim is to study the convergence for iterates of Lupaşş (p, q)-Bernstein operators using the contraction principle
4 Iterates of Lupas (p, q)-Bernstein operator we extend the study of the iterates of Bernstein operators in the framework of (p, q)calculus
Summary
⎨1 ⎩(x a)(x qa) qn–1 a) if n = 0, if n ≥ 1. It is established by induction that k k q fi (–1)r q r(r–1) 2 r=0 k r fi+k–r (see [36] and [17]). Note that (1.2) may be written in the q-difference form nn
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