$q$-GENERALIZATIONS OF THE PICARD AND GAUSS-WEIERSTRASS SINGULAR INTEGRALS
$q$-GENERALIZATIONS OF THE PICARD AND GAUSS-WEIERSTRASS SINGULAR INTEGRALS
Introducing a higher order modulus of smoothness based on $q$-integers, in this paper first we obtain Jackson-type estimates in approximation by Jackson-type generalizations of the $q$-Picard and $q$-Gauss-Weierstrass singular integrals and give their global smoothness preservation property with respect to the uniform norm. Then, we study approximation and geometric properties …