Kodai Mathematical Journal

On deviations, small functions and strong asymptotic functions of meromorphic functions

Ewa Ciechanowicz and Ivan Ivanovich Marchenko

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Abstract

The paper addresses two long-standing problems: of extending the second main theorem of Nevanlinna to the case of small functions, and of finding an upper limit for the number of asymptotic functions of a function of finite lower order. Upper estimates of the sum of deviations and the numbers of strong asymptotic functions and strong functional asymptotic spots of meromorphic functions of finite lower order are presented. The structure of the set of Petrenko's deviations from small functions for meromorphic functions of finite lower order is examined. An analogue of Denjoy's question for strong asymptotic small functions of meromorphic functions of finite lower order is also considered.

Article information

Source
Kodai Math. J., Volume 40, Number 2 (2017), 379-404.

Dates
First available in Project Euclid: 12 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1499846603

Digital Object Identifier
doi:10.2996/kmj/1499846603

Mathematical Reviews number (MathSciNet)
MR3680567

Zentralblatt MATH identifier
1373.30035

Citation

Ciechanowicz, Ewa; Marchenko, Ivan Ivanovich. On deviations, small functions and strong asymptotic functions of meromorphic functions. Kodai Math. J. 40 (2017), no. 2, 379--404. doi:10.2996/kmj/1499846603. https://projecteuclid.org/euclid.kmj/1499846603


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