Abstract. In this paper, we present some general results on the pointwise convergence of the non-convolution type nonlinear singular integral operators in the following form:

We will prove some theorems concerning pointwise convergence of the family L (!; x) as ! 1 at a …xed point x 2 D which represents any generalized Lebesgue point of the function ! 2 L 1 (D) ; where D is an open bounded subset of R n : Moreover, we will consider the case D = R n :

In this study, we introduce a new kind of nonlinear Bernstein-Chlodowsky operators based on q-integers. Firstly, we define the nonlinear q?Bernstein-Chlodowsky operators of max-product kind. Then, we give an error estimation for the q?Bernstein Chlodowsky operators of max-product kind by using a suitable generalizition of the Shisha-Mond Theorem. There follows an upper estimates of the approximation error for some subclasses of functions.

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