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On the Mellin-Gauss-Weierstrass operators in the Mellin-Lebesgue spaces
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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 $f$.
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
Title: On the Mellin-Gauss-Weierstrass operators in the Mellin-Lebesgue spaces
Description:
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 $f$.
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