No abstract

In this paper we introduce a general class of integral operators that fix exponential functions, containing several recent modified operators of Gauss–Weierstrass, or Picard or moment type operators. Pointwise convergence theorems are studied, using a Korovkin-type theorem and a Voronovskaja-type formula is obtained.

This study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted modulus of continuity, the result regarding global smoothness preservation properties for the generalized Picard operators, which based in Agratini et al.

In this paper, we prove some results on convergence properties of higher order partial derivatives of multidimensional convolution-type singular integral operators being applied to the class of functions which are integrable in the sense of Lebesgue.

In this paper, we present some approximation properties of the Gauss-Weierstrass operators in exponential weighted spaces including norm convergence of them and Voronovskaya and quantitative Voronovskaya-type theorems.