In the present paper, we consider the complete asymptotic expansion of certain exponential-type operators connected with $$2x^{3/2}$$ 2 x 3 / 2 . Also, a modification of such exponential-type operators is provided, which preserve the function $$\mathrm{e}^{Ax}$$ e Ax .

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In this paper we consider a link B n,ρ between Baskakov type operators B n,∞ and genuine Baskakov-Durrmeyer type operators B n,1 depending on a positive real parameter ρ. The topic of the present paper is the pointwise limit relation B n,ρ f (x) → B n,∞ f (x) as ρ → ∞ for x ≥ 0. As a main result we derive uniform convergence on each compact subinterval of the positive real axis for all continuous functions f of polynomial growth.

The purpose of this paper is the evaluation of the Fourier transform of powers of the sinc function multiplied by monomials, also in the cases when log terms arise. Such evaluations appear only rarely in the literature. Some old sources are hardly available. Because of notations not in use today, several original works are difficult to read. We apply an approach by J. H. Michell in a variant of G. H. Hardy to integrals over sinc powers and their Fourier transforms. Moreover, the connection of such integrals with B‑splines is accentuated.