On the Mellin-Gauss-Weierstrass operators in the Mellin-Lebesgue spaces

In this paper, we present the modulus of smoothness of a function f∈Xcᵖ, which the Mellin-Lebesgue space, and later we state some properties of it. In this way, the rate of convergence is gained. Moreover, we elucidate some pointwise convergence results for the Mellin-Gauss-Weierstrass operators. Especially, we acquire the pointwise convergence of them at any Lebesgue point of a function f.