Purpose: The purpose of this paper is to introduce the mixed summation-integral-type Lupaş-Phillips-Bernstein operators. Methods: Firstly, we compute the moments of the operators. We use the method of Korovkin-type statistical approximation and modulus of continuity. Results: We find the rate of convergence of the modified operators using statistical convergence and modulus of continuity. Concl...

The goal of this paper is to give a form the operator involving generating function Apostol-Genocchi polynomials order α. Applying Korovkin theorem, we arrive at convergence with aid moments and central moments. We determine rate using several tools such as -functional, modulus continuity, second continuity. also type Voronovskaya theorem for estimating error. Moreover, investigate some results...

In this paper, we discuss properties of convergence for a modification of the q-Bernstein operators. Using the notion of A-statistical approximation, where A is a nonnegative regular summability matrix, we investigate the Korovkin type statistical approximation properties of this modification via A-statistical approximation. For 0 < q ≤ 1, we obtain that the q-Bernstein operators is A-statistic...

In the present paper, we introduce a Laguerre type positive linear operators based on the q-integers including the q-Meyer König and Zeller operators defined by Doğru and Duman in [7]. Then we obtain some results about Korovkin type approximation properties and rates of convergence for this generalization. Key-Words: Positive linear operators, q-Meyer König and Zeller operators, qLaguerre polyn...