Loading [MathJax]/jax/output/SVG/config.js
Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 230, Pages 56–74
DOI: https://doi.org/10.36535/0233-6723-2023-230-56-74
(Mi into1245)
 

On the proximate growth function relative to the model growth function

M. V. Kabankoa, K. G. Malyutina, B. N. Khabibullinb

a Kursk State University
b Institute of Mathematics and Computing Centre of Ural Branch of Russian Academy of Sciences
References:
Abstract: The concept of proximate order is widely used in the theories of integer, meromorphic, subharmonic, and plurisubharmonic functions. In this paper, we provide a general interpretation of this concept as a proximate growth function relative to the model growth function. The classical proximate order is the proximate order in the sense of Valiron. Our definition uses only one condition. This form of definition is new for the classical proximate order. In this review, we show that for any function defined on a positive ray whose growth is determined by a model growth function, there is a proximate growth function relative to the model growth function.
Keywords: Hadamard problem, model growth function, proximate order, convex function, entire function, subharmonic function.
Funding agency Grant number
Russian Science Foundation 22-21-00012
Ministry of Science and Higher Education of the Russian Federation FMRS-2022-0124
The work of K. G. Malyutin was supported by the Russian Science Foundation (project № 22-21-00012). The work of B. N. Khabibullina was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of the Russian Federation (scientific topic code FMRS-2022-0124).
Document Type: Article
UDC: 517.51, 517.53
MSC: 26A12, 30D15, 26A48
Language: Russian
Citation: M. V. Kabanko, K. G. Malyutin, B. N. Khabibullin, “On the proximate growth function relative to the model growth function”, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 230, VINITI, Moscow, 2023, 56–74
Citation in format AMSBIB
\Bibitem{KabMalKha23}
\by M.~V.~Kabanko, K.~G.~Malyutin, B.~N.~Khabibullin
\paper On the proximate growth function relative to the model growth function
\inbook Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 1
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 230
\pages 56--74
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1245}
\crossref{https://doi.org/10.36535/0233-6723-2023-230-56-74}
Linking options:
  • https://www.mathnet.ru/eng/into1245
  • https://www.mathnet.ru/eng/into/v230/p56
  • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
    Statistics & downloads:
    Abstract page:96
    Full-text PDF :31
    References:30
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025