<i>m</i>-th order exponential sampling Kantorovich series

In the present paper, we define and study a new family of sampling-type operators. By composing C. Bardaro's well-known generalized exponential sampling operators with Mellin differential and Mellin anti-differential operators of order m, we derive the m-th order Kantorovich-type exponential sampling series. This family of operators is highly general and encompasses, as special cases, the well-known exponential sampling Kantorovich operators. Here, the pointwise and uniform convergence of m-th order Kantorovich-type exponential sampling series is investigated. Additionally, quantitative estimates on the rate of approximation, asymptotic formulae, and Voronovskaya-type theorems are established. The derivation of these results relies significantly on certain algebraic moments of the associated kernels, which can be computed using the Mellin-Fourier transform (or, more concisely, the Mellin transform) and the well-known Mellin-Poisson summation formula. Thanks to the aforementioned results, the simultaneous approximation of a function and its Mellin derivatives can be addressed both qualitatively and quantitatively.