We describe a unifying approach for studying the power series of the positive linear operators from a certain class. For the same operators, we give simpler proofs of some known ergodic theorems.

In this paper we consider two different general linear positive operators defined on unbounded interval and obtain estimates for the differences of these operators in quantitative form. Our estimates involve an appropriate ...

This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, 10.1007/s00009-016-0804-7) where Szasz-Mirakyan operators preserving exponential functions are defined. As a first result, we show that the ...

Since the introduction of Bernstein operators, many authors defined and/or studied Bernstein type operators and their generalizations, among them are Morigi and Neamtu (Adv Comput Math 12:133-149, 2000). They proposed an ...

In this paper, we study the k-th order Kantorovich type modication of Szasz-Mirakyan operators. We first establish explicit formulas giving the images of monomials and the moments up to order six. Using this modification, ...

The Voronovskaya theorem which is one of the most important pointwise convergence results in the theory of approximation by linear positive operators (l.p.o) is considered in quantitative form. Most of the results presented ...

The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative ...

In this paper we investigate the power series of Beta operators. We first study the convergence of this series and describe the Voronovskaya operator A and the inverse Voronovskaya operator. Then, a quantitative convergence ...