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We introduce a new sequence of linear positive operators by combining the Charlier polynomials and the Szász type operators defined by Jain (in J Aust Math Soc 13(3):271–276, 1972). We obtain the degree of approximation of these operators by means of the weighted modulus of continuity and for functions in a Lipschitz type space. We also study the approximation of functions having a derivative equivalent with a function of bounded variation. [ABSTRACT FROM AUTHOR]

Recently, a mixed hybrid operator, generalizing the well-known Phillips operators and Baskakov–Szász type operators, was introduced. In this paper, we study Bézier variant of these new operators. We investigate the degree of approximation of these operators by means of the Lipschitz class function, the modulus of continuity, and a weighted space. We study a direct approximation theorem by means of the unified Ditzian–Totik modulus of smoothness. Furthermore, the rate of convergence for functions having derivatives of bounded variation is discussed. [ABSTRACT FROM AUTHOR]

We consider a combination of Chlodowsky polynomials with generalized Szasz operators involving Charlier polynomials. We give the degree of approximation for these bivariate operators by means of the complete and partial modulus of continuity, and also by using weighted modulus of continuity. Furthermore, we construct a GBS (Generalized Boolean Sum) operator of bivariate Chlodowsky-Szasz-Charlier type and estimate the order of approximation in terms of mixed modulus of continuity. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce the q-analog of the Stancu variant of Szász-Baskakov operators. We establish the moments of the operators by using the q-derivatives and then prove the basic convergence theorem. Next, the Voronovskaja type theorem and some direct results for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Lastly, we study the A-statistical convergence of these operators and also, in order to obtain a better approximation, we study a King type modification of the above operators. [ABSTRACT FROM AUTHOR]