On Linear Positive Operators Involving Biorthogonal Polynomials

Abstract

In this paper, we recall Konhauser polynomials. Approximation properties of these operators are obtained with the help of the Korovkin theorem. The order of convergence of these operators is computed by means of modulus of continuity, Peetre’s K-functional, and the elements of the Lipschitz class. Also, we introduce the $r$-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally, we give an application to differential equations.