Issue №: 8 (48)
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.
THE DEVELOPMENT OF THE CONCEPT OF ELASTICITY
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.
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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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