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In this paper, we define a new kind of the μ -Bernstein–Schurer–Stancu operators. For these operators, we prove uniform convergence and study their behavior using consideration modulus of continuity and smoothness. Moreover, we present the Korovkin type theorem, Voronovskaya type theorem, and Grüss–Voronovskaya type theorems. [ABSTRACT FROM AUTHOR]

In this paper we study a notion called (E, 1)(C, 1)−weighted statistical convergence and prove a Korovkin type approximation theorem. The rate of convergence for weighted statistical convergence is obtained. In the last section we also give Voronovskaya and Grüss‐Voronovskaya type theorems and some illustrative numerical examples [ABSTRACT FROM AUTHOR]

In this paper, we study the Kantorovich variant of Szász operators based on Sheffer polynomials and prove a Korovkin type theorem. Also, we present the Voronovskaya type theorem and Grüss-Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result. [ABSTRACT FROM AUTHOR]

In this paper we will prove the Korovkin type theorem for modified Szász–Mirakyan operators via A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss–Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this paper some properties of the generalized Szasz operators by multiple Appell polynomials are given, using into consideration the power summability method. In the first section are given some direct estimation related to the generalized Szasz operators by multiple Appell polynomials, including Korovkin type theorem. In the second section, we give some results related to the weighted spaces of continuous functions and Voronovskaya type theorem. In the third section, we have proved some results related to the statistical convergence of the generalized Szasz operators by multiple Appell polynomials, using into consideration the A− transformation. At the end of the paper are given some illustrative computational examples which make such summability methods (for example, power series method) more useful and fruitful for applications of functional analysis in approximation theory. [ABSTRACT FROM AUTHOR]

In this paper we will prove the Korovkin type theorem for Baskakov-Schurer-Szász operators via the A-statistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods and in the last chapter we give a kind of Voronovskaya type theorem for the A-statistical convergence and Grüss-Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this paper we will prove the Korovkin type theorem for new modified Szász-Mirakyan operators via A-statistical convergence and power summability method. Also we give the rate of the convergence related to the summability methods and in the last section we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a new class of the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators, which considerably extends the well-known class of the classical Baskakov-Schurer-Szász-Stancu approximation operators. For this new class of approximation operators, we present a Korovkin type theorem and a Grüss-Voronovskaya type theorem, and also study the rate of its convergence. Moreover, we derive several results which are related to the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators in the weighted spaces. Finally, we prove some shape-preserving properties for the parametric generalization of the Baskakov-Schurer-Szász-Stancu operators and, as a special case, we deduce the corresponding shape-preserving properties for the classical Baskakov-Schurer-Szász-Stancu approximation operators. [ABSTRACT FROM AUTHOR]