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Journal of Automation and Information Sciences
SJR: 0.238 SNIP: 0.464 CiteScore™: 0.27

ISSN Печать: 1064-2315
ISSN Онлайн: 2163-9337

Выпуски:
Том 51, 2019 Том 50, 2018 Том 49, 2017 Том 48, 2016 Том 47, 2015 Том 46, 2014 Том 45, 2013 Том 44, 2012 Том 43, 2011 Том 42, 2010 Том 41, 2009 Том 40, 2008 Том 39, 2007 Том 38, 2006 Том 37, 2005 Том 36, 2004 Том 35, 2003 Том 34, 2002 Том 33, 2001 Том 32, 2000 Том 31, 1999 Том 30, 1998 Том 29, 1997 Том 28, 1996

Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v51.i4.40
pages 43-54

Approximative Properties of the Generalized Poissin Integrals on the Classes of Functions Determined by a Modulus of Continuity

Yuriy I. Kharkevych
Lesya Ukrainka Eastern European National University, Lutsk

Краткое описание

One of the most important problems of applied mathematics is to study various problems of natural science which ultimately lead to compilation of mathematical models of phenomena under study. Moreover these mathematical models will be of practical interest if and only if they adequately reflect real situations. Very often the objects studied are extremely complex. In such cases some other method can be a real find for obtaining an additional information about this quantity, allowing its solution to be obtained at least approximately. In this case it is advisable to apply the methods and approaches of the theory of function approximation, namely, the asymptotic estimates. The theory of functions approximation is important because it gives general grounds for practical calculation of functions for the approximate replacement of complex functions by simpler ones. In this case an important role is played by the modulus of continuity which characterizes the maximum absolute increment of the function studied between the points of the definition domain. Also of importance are the classes of functions defined by the modulus of continuity, in particular, the Hölder classes. This paper studies the problem of finding the exact upper bound of deviation of functions classes that are determined by the first order modulus of continuity from their generalized Poisson integrals. In a particular case there were obtained the asymptotic equalities for approximating functions of Hölder classes by their generalized Poisson integrals. Thereby it was shown that a transition from classes Hω to more "susceptible" Hölder classes of functions H1 provided more qualitative solution of Kolmogorov−Nikolskii problem for generalized Poisson integrals in a uniform metric that has a direct application in mathematical modeling and mathematical formalizations in certain types of problems in a game theory.

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