Economy, finances, management: Topical issues of science and practical activity


Issue №: 8 (48)

Published: 2019.09.17
DOI: 10.37128/2411-4413-2019-8

The magazine deals with the problems of the agricultural sector of the economy in the context of integration and processes of globalization. Attention is paid to the issues of development of digital economy, rural territories, technologies of enterprise management and organization of accounting, problems of legal support of economic processes, market tendencies of development of various branches of economy. Particular attention is paid to green tourism as a promising segment of the national economy.

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DOI: 10.37128/2411-4413-2019-8-5
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NAIKO  Dmytro  –  Candidate of Physical and Mathematical Sciences, Associate 

Professor,Vinnytsia National Agrarian University (21008, Vinnytsia, 3, Soniachna Str: e-mail: 

dmnaiko@ukr.net ).

SHEVCHUK Olena  –  Candidate of  Economic  Sciences, Associate Professor,Vinnytsia National 

Agrarian University (21008, Vinnytsia, 3, Soniachna Str: e-mail: lsd77@ukr.net).


In addition to the methods of classical mathematical analysis, which are widely used in economic 

modeling, there are methods of quantum analysis or q-analysis, which have already penetrated into many 

theoretical and applied  branches of mathematics. The fundamental difference between quantum analysis 

and classical analysis is that in it the notion of derivative is not considered as the limit of the ratio of two 

infinitely small quantities.

Changing the approach to the definition of a derivative led to another differential calculus, which 

is called q-calculus.

In this paper, we show what kind of q-analogues of the most well-known mathematical facts of 

classical mathematical analysis have and we partially demonstrate the method  of their derivations. We 

note some areas of q-analysis implementation in applied mathematics and mathematical physics. 

We introduce into consideration the q-analogue of such a notion of an economic 

modelingaselasticity. We study its properties and calculate the q-elasticity of some elementary functions. 

We carry out a comparative analysis of the classical coefficient of elasticity with the q-coefficient of 

elasticity. The concept of q-elasticity is new and not previously encountered in the scientific literature.

Keywords: q-analysis, q-analog, q-derivative, q-exponent, q-elasticity, economic modeling.

List of references

1.  KolemaevV.  A. (2012).  Matematycheskaia  ekonomyka  [Mathematical  economics]  .M.: 

YuNYTY-DANA (in Russian).

2. Kolemaev V. A. & V. Y. Malykhyn (1999).  Matematycheskye  metody  pryniatyia  reshenyi v 

ekonomyke [Mathematical methods of decision-making in the economy]. M.: Fynstatynform (in Russian).

3. Shevchuk O. D.&  D. A. Naiko.  (2017).  Metody matematychnoho analizu ta kontroliu riznykh etapiv 

infliatsiinoho protsesu  [Methods of mathematical analysis and control of various stages of the inflation process]. 

Suchasni informatsiini tekhnolohii ta innovatsiini metody navchannia u pidhotovtsi fakhivtsiv: metodolohiia, 

teoriia, dosvid, problemy−Modern information technologies and innovative methods of training in the training of 

specialists: methodology, theory, experience, problems. 49. 171 –  177  (in Ukrainian).

4. V.G. Kac& P. Cheung. (2002). Quantum Calculus. Universitext, Sprinqer-Verlag, New-York.

5. Aral Ali, Gupta Vijay & Agarwal Ravi P. (2013). Applicationsof q-Calculus in Operator Theory. 

Sprinqer-Verlag, New-York.

6. George E. Andrews, Richard Askey  &  Ranjan Roy. (1999).  Special Functions.  Cambridge U. 

Press, Cambridge.

7. Phillips G. M.(1997). Bernstein polynomials based on the q- integers. Ann. Numer. Math. 4.258 –264.

8. Oruc H.  &  Tuncer N.  (2002).  On the convergence and iterates of  q-Bernstein polynomials .  J. 

Approx. Theory. 117. 301–313.

9. Ostrovska S.  (2006).  On the improvement of analytic properties under the limit  q-Bernstein 

operator. Approx. Theory. 138. 37–53. 

10. Naiko D.A. (2016). Pro deiaki aproksymatsiini vlastyvosti  q-parametrychnykh mnohochleniv 

Bernshteina [On  some  approximation  properties  of  q-Bernstein  polynomials].  Zbirnyk prats In-tu 

matematyky NAN Ukrainy–Proceedings of the Institute of Mathematics of the National Academy of 

Sciences of Ukraine. 13(2). 214−226 (in Ukrainian).

11. Naiko D. A. (2018).  Dodatni operatory klasu  B  ta yikhni kombinatsii: Monohrafiia  [Positive

operators of B-class and their combinations: Monograph]. Vinnytsia: VNAU (in Ukrainian).

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About journal

Topics of the journal:

051 Economics

071 Accounting and taxation

072 Finance, banking and insurance

073 Management

075 Marketing

076 Business, trade and exchange activities

241 Hotel, restaurant and catering 

281 Public administration


Key information:
ISSN (print): 2411-4413
DOI: 10.37128

The journal “Economy, finances, management: Topical issues of science and practice” is included in the "List of Scientific Professional Editions of Ukraine". 

The scientific edition is assigned the Category "Б" in the field of economics in specialties 051, 071, 072, 073, 075, 076, 241, 281

(Order of the Ministry of Education and Science of Ukraine No. 249, March 17, 2020).

The journal “Economy, finances, management: Topical issues of science and practice” has a Digital Object Identifier (DOI)

The journal “Economy, finances, management: Topical issues of science and practice” is indexed in such database as Index Copernicus Value (https://journals.indexcopernicus.com/search/form)


The editorial board of the journal is guided by the principles of scientific, objectivity, professionalism, informational support of the most significant innovative researches, observance of standards of publishing ethics.

The purpose of the journal "Economics, finances, management: Topical issues of science and practical activity» is the coverage of leading scientific ideas in the economic, financial and management activities of the sectors of the national economy and the involvement of representatives of the domestic and foreign scientific professional community.


Objectives of the journal:

  • publication of research findings on innovation in the economy, financial and management spheres, innovation of production processes;
  • expanding partnerships with international scientific publishing organizations;
  • enhancing the culture of reviewing and annotating published material;
  • adherence to editorial ethics.


Article publishing is a paid service. Cost for printing in professional publications in accordance with the Decree of the Cabinet of Ministers of Ukraine of August 27, 2010 No. 796 "On approval of the list of paid services that can be provided by state educational institutions, other institutions of the educational system belonging to state and communal ownership" and the order Rector of the Higher Education University Mazura VA dated March 14, 2018 No. 93 “On setting the cost of printing in professional editions of the University”.

The cost of printing one page in professional editions of the university is 60 UAH.

An additional copy of the magazine with the mailing list costs 250 UAH.

Recipient: Vinnytsia National Agrarian University MFO 820172 Current account No. 31256282102055 Code 00497236 Bank State Treasury Service of Ukraine, Kyiv. VAT payer code 004972302286. Registration number 100271744. Purpose of payment: for printing an article in the journal: ”Economy, finances, management: Topical issues of science and practical activity "

History of journal:

It was founded in 1997 under the name "Bulletin of the Vinnytsia State Agricultural Institute". In 2010-2014 he was published under the title “Collection of scientific works of Vinnitsa National Agrarian University”.

From 2015 ”Economy, finances, management: Topical issues of science and practical activity” (Certificate of State Registration of Mass Media No. 21154-10954 of PR as of December 31, 2014)

The journal is the successor to the edition ”Collection of Scientific Papers of Vinnytsia National Agrarian University. Series: Economic Sciences. "