Approximation Operators of Binomial Type

Sheffer polynomials and approximation operators

“…and let P be the linear operator defined by P = xQ ′−1 . Using the method from [4] or [6] and the identity…”

“…have been studied in [1]- [2], [4]- [8], [10]- [11]. Next we consider a Sheffer set relative to Q, namely s 0 (x) = c = 0 and Qs n (x) = ns n−1 (x).…”

Structure Properties for Binomial Operators

“…As an extension to the well-known Bernstein operators, binomial operators are defined as follows (see [1], [2], or [3]):…”

“…In the next section, we introduce some primary concepts and results involved in this paper, which can be found in [1,2,17].…”

Umbral interpolation

“…We will call this problem umbral interpolation problem, because its solution can be expressed by a basis of Sheffer polynomials, also said umbral basis. Interpolation and approximation have been studied from an umbral point of view in several papers [10,15,17]. In [18,19] the authors study the sequence of polynomials, which solve the linear interpolation in P n , but not the general case, moreover no connection with real function is given.…”