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UDC 519.8
Yu.I. Kharkevych1, O.G. Khanin2


1 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 kharkevich.juriy@gmail.com

2 Lesya Ukrainka Volyn National University, Lutsk, Ukraine

 aleks.hanin@gmail.com

ASYMPTOTIC PROPERTIES OF THE SOLUTIONS OF HIGHER-ORDER
DIFFERENTIAL EQUATIONS ON GENERALIZED HLDER CLASSES

Abstract. Some asymptotic properties of the solutions of elliptic-type differential equations are investigated using the methods of approximation theory. The approximation characteristics of Poisson-type operators as solutions of higher-order differential equations on generalized Holder classes in a uniform metric have been investigated. In particular, the Kolmogorov–Nikol’skii problem (in O.I. Stepanets terminology) of finding the upper bounds for the deviations of functions defined by the modulus of continuity from the Abel–Poisson and Gauss–Weierstrass operators in the space metric is solved. The above-mentioned operators are one of the efficient tools for the analysis of the mathematical models that arise when solving many applied optimization problems.

Keywords: optimization properties of functions, approximative characteristics, Kolmogorov– Nikol’skii problem, Abel–Poisson operator, Gauss–Weierstrass operator, Holder classes .


full text

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