Modifying an approximation process using non-Newtonian calculus


In the present note we modify a linear positive Markov process of discrete type by using so called multiplicative calculus. In this framework, a convergence property and the error of approximation are established. In the final part some numerical examples are delivered.


O. Agratini
Babes-Bolyai University, Faculty of Mathematics and Computer Science, Cluj-Napoca, Romania
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy, Cluj-Napoca, Romania

H. Karsli
Bolu Abant Izzet Baysal University, Faculty of Science and Arts, Department of Mathematics, Golkoy Bolu, Turkey


Linear positive operator; non-Newtonian calculus; modulus of multiplicative smoothness.


See the expanding block below.

Paper coordinates

O. Agratini, Modifying an approximation process using non-Newtonian calculus, Stud. Univ. Babes-Bolyai Math. 65 (2020) no. 2, 291–301, doi: 10.24193/subbmath.2020.2.10


About this paper


Studia Univ. Babes-Bolyai, Mathematica

Publisher Name

Babes-Bolyai University

Print ISSN
Online ISSN


Google Scholar Profile


[1] Bashirov, A.E., Kurpinar, E.M., Ozyapici, A., Multiplicative calculus and its applications, J. Math. Anal. Appl., 337(2008), 36-48.
[2] Cai, Q.-Bo, Zhou, G., Li, J., Statistical approximation properties of λ-Bernstein operators based on q-integers, Open Math., 17(2019), no. 1, 487-498
[3] Catina¸s, T., Some classes of surfaces generated by Nielson and Marshall type operators on the triangle with one curved side, Stud. Univ. Babes-Bolyai Math., 61(2016), no. 3, 305-314.
[4] Filip, D.A., Piatecki, C., A non-newtonian examination of the theory of exogenous economic growth, Mathematica Aeterna, 4(2014), no. 2, 101-117.
[5] Grossman, M., Katz, R., Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
[6] Gupta, V., Agrawal, G., Approximation for link Ismail-May operators, Ann. Funct. Anal.,, online: 13 January 2020.
[7] Mursaleen, M., Rahman, S., Ansari, K.J., Approximation by Jakimovski-LeviatanStancu-Durrmeyer type operators, Filomat, 33(2019), no. 6, 1517-1530.
[8] Stanley, D., A multiplicative calculus, Primus: Problems, Resources, and Issues in Mathematics Undergraduate Studies, 9(1999), no. 4, 310-326.

Related Posts