Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

The approximation of bivariate Chlodowsky-Szász-Kantorovich-Charlier-type operators

In this paper, we introduce a bivariate Kantorovich variant of combination of Szász and Chlodowsky operators based on Charlier polynomials. Then, we study local approximation properties for these operators. Also, we estimate the approximation order in terms of Peetre's K-functional and partial moduli of continuity. Furthermore, we introduce the associated GBS-case (Generalized Boolean Sum) of t...

Rate of convergence by Kantorovich-Szász type operators based on Brenke type polynomials

The present paper deals with the approximation properties of the univariate operators which are the generalization of the Kantorovich-Szász type operators involving Brenke type polynomials. We investigate the order of convergence by using Peetre's K-functional and the Ditzian-Totik modulus of smoothness and study the degree of approximation of the univariate operators for continuous functions i...

Approximation by Lupas-Type Operators and Szász-Mirakyan-Type Operators

Szász-Durrmeyer operators involving Boas-Buck polynomials of blending type

The present paper introduces the Szász-Durrmeyer type operators based on Boas-Buck type polynomials which include Brenke type polynomials, Sheffer polynomials and Appell polynomials considered by Sucu et al. (Abstr. Appl. Anal. 2012:680340, 2012). We establish the moments of the operator and a Voronvskaja type asymptotic theorem and then proceed to studying the convergence of the operators with...

Multivariate Expansion Associated with Sheffer-type Polynomials and Operators

With the aid of multivariate Sheffer-type polynomials and differential operators, this paper provides two kinds of general expansion formulas, called respectively the first expansion formula and the second expansion formula, that yield a constructive solution to the problem of the expansion of A(t̂)f(ĝ(t)) (a composition of any given formal power series) and the expansion of the multivariate ent...