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Ufimsk. Mat. Zh., 2017, Volume 9, Issue 3, Pages 18–26 (Mi ufa381)  

Two-sided estimates for the relative growth of functions and their derivatives

G. G. Braichev

Moscow State Pedagogical University, M. Pirogovskaya str. 1, 199296, Moscow, Russia

Abstract: We provide an extended presentation of a talk given at the International mathematical conference on theory of functions dedicated to centenary of corresponding member of AS USSR A. F. Leont'ev. We propose a new method for obtaining uniform two-sided estimates for the fraction of the derivatives of two real functions on the base of the information of two-sided estimates for the functions themselves. At that, one of the functions possesses certain properties and serves as a reference for measuring a growth and introduces some scale. The other function, whose growth is compared with that of the reference function, is convex, increases unboundedly or decays to zero on a certain interval. The method is also applicable to some class of functions concave on an interval. We consider examples of applications of the obtained results to the behavior of entire functions.

Keywords: monotone function, convex function, relative growth of two functions, uniform upper and lower estimates, entire function.

Full text: PDF file (314 kB)
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English version:
Ufa Mathematical Journal, 2017, 9:3, 18–25 (PDF, 293 kB); https://doi.org/10.13108/2017-9-3-18

Bibliographic databases:

UDC: 517.272+517.518.244+517.547.22
MSC: 26D10, 30D15
Received: 03.06.2017

Citation: G. G. Braichev, “Two-sided estimates for the relative growth of functions and their derivatives”, Ufimsk. Mat. Zh., 9:3 (2017), 18–26; Ufa Math. J., 9:3 (2017), 18–25

Citation in format AMSBIB
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\pages 18--26
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