On the generalized Picard and Gauss Weierstrass singular integrals
Özet
In this paper, we give the generalizations of the Picard and the Gauss Weierstrass singular integral operators which are based on the q-numbers and depend on q-generalization of the Euler gamma integral. Later on, some approximation properties of these two generalized operators are established in L-p (R) and weighted -L-p (R) spaces. We also show that the rates of convergence of these generalized operators to approximating function f in the L-p-norm are at least so faster than that of the classical Picard and Gauss Weierstrass singular integral operators.