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Doklady Mathematics - Two classes of Taylor-type formulas for arbitrary continuous functions on intervals are obtained using Bernstein polynomials. These formulas are applicable to both smooth... 相似文献
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Doklady Mathematics - This paper contains results concerning superreflective Besov spaces $$B_{{p,q}}^{s}({{\mathbb{R}}^{n}})$$ . Namely, expressions for convexity moduli and smoothness moduli with... 相似文献
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A. N. Agadzhanov 《Doklady Mathematics》2018,97(3):219-222
The class of everywhere differentiable functions without monotonicity intervals is considered in terms of number theory. A number-theoretic representation of the set of points of the unit interval is constructed using the classification of transcendental numbers proposed by K. Mahler, and a theorem on sufficient conditions for differentiable functions to belong to this class is stated. Results concerning the behavior of derivatives of functions from this class are presented. A mixed problem for the heat equation modeling heat transfer in a distributed system is considered. It is shown that the control function for this system can be everywhere differentiable but having no monotonicity intervals. 相似文献
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