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

Year 2024, Volume: 73 Issue: 3, 630 - 640, 27.09.2024

Fırat Özsaraç

https://doi.org/10.31801/cfsuasmas.1455235

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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