We consider a variant En,k (N; r, r; p, p) of the four-parameter Stechkin problem En,k (N; r, s; p, q) on the best approximation of differentiation operators of order k on the class of n times differentiable functions (0 < k < n) in Lebesgue spaces on the real axis. We discuss the state of research in this problem and related problems in the spaces of multipliers of Lebesgue spaces and their predual spaces. We give two-sided estimates for En,k (N; r, r; p, p). The paper is based on the author’s talk at the S.B.Stechkin’s International Workshop-Conference on Function Theory (Kyshtym, Chelyabinsk region, August 1–10, 2023). © 2023, Krasovskii Institute of Mathematics and Mechanics. All rights reserved.