A note on the modified Picard integral operators

Abstract

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.

On Certain Multidimensional Nonlinear Integrals

“…Also, results and applications in wide range concerning linear operators can be found in [1,4,8,12,17,20]. Some weighted approximation results concerning well-known Gauss-Weierstrass and Picard integral operators can be found in the recent articles [23] and [24], respectively. In [16], a class of summation-integral-type operators covering many well-known ones was considered.…”