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In this paper, we present the modulus of smoothness of a function f∈X₂^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.
Fırat Özsaraç (Fri,) studied this question.