On the Mellin-Gauss-Weierstrass operators preserving logarithmic functions in the weighted Mellin-Lebesgue spaces

In the present paper, we state a quantitative version of the convergence utilizing the logarithmic weighted modulus of continuity for a new generalization of the Mellin-Gauss-Weierstrass operators which preserve logarithmic functions. Later, we express logarithmic moments of the modified operators, and then we give Voronovskaya-type theorem. Moreover, a rate of convergence is achieved, and onwards the global smoothness preservation feature is stated via the logarithmic weighted modulus of continuity in the weighted Mellin-Lebesgue spaces comprising all Lebesgue measurable functions.