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

Abstract

In this paper, we present the modulus of smoothness of a function $f∈X_{c}^{p}$, 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 $f$.

Keywords

• Mellin-Gauss-Weierstrass operators
• Mellin-Lebesgue spaces
• modulus of smoothness
• Lebesgue point

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