Abstract
In this paper, we present the solution to Stechkin’s problem for differential operators and functionals of first and second orders on the class of functions that are defined on a finite interval and have bounded third derivative. Two related problems are discussed: (1) finding sharp constants in the Landau–Kolmogorov inequalities, and (2) optimal recovery of an operator with the help of a set of linear operators (or arbitrary single-valued mappings) on elements of some set that are given with an error.
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