Research Article

Nonlinear Approximation by $q$-Favard-Sz{\'a}sz-Mirakjan Operators of Max-Product Kind

Volume: 6 Number: 2 June 30, 2023
EN

Nonlinear Approximation by $q$-Favard-Sz{\'a}sz-Mirakjan Operators of Max-Product Kind

Abstract

In this study, nonlinear $q$-Favard-Sz{\'a}sz-Mirakjan operators of max-product kind are defined and approximation properties of these operators are investigated. Classical approximation and $A$-statistical approximation theorems are given.

Keywords

Favard-Szász-Mirakjan operators , Modulus of continuity , Nonlinear max-product operators , $q$-integers

References

  1. [1] A. Lupas, A q-analogue of the Bernstein operator, in Seminar on Numerical and Statistical Calculus, University of Cluj-Napoca, 9 (1987), 85–92.
  2. [2] G.M. Philips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.
  3. [3] S. Ostrovska, q-Bernstein polynomials and their iterates, J. Approximation Theory, 123(2) (2003), 232-255.
  4. [4] S. Ostrovska, On the Lupas q-analogue of the Bernstein operator, Rocky Mountain. J. Math., 36(5) (1997), 1615-1629.
  5. [5] H. Oruc, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory, 117 (2002), 301-313.
  6. [6] M.A. Siddigue, R.R. Aqrawal, N. Gupta, On a class of new Bernstein operators, Advanced Studies in Contemporary Mathematics, 2015.
  7. [7] D. Karahan, A. Izgi, On approximation properties of generalized q-Bernstein operators, Num. Funct. Anal. Opt., 39 (2018), 990-998.
  8. [8] D. Karahan, A. Izgi, On approximation properties of (p;q)-Bernstein operators, Eur. J. of Pure and App. Math., 11 (2018), 457-467.
  9. [9] B. Bede, L. Coroianu, S.G. Gal, Approximation by max-product type operators, Springer International Publishing Switzerland, 2016.
  10. [10] B. Bede, L. Coroianu, S.G. Gal, Approximation by truncated Favard-Sz´asz-Mirakjan operator of max-product kind, Demonstratio Math. 44 (2011), 105-122.
APA
Karahan, D., & Acar, E. (2023). Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences, 6(2), 104-114. https://doi.org/10.33434/cams.1242905
AMA
1.Karahan D, Acar E. Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences. 2023;6(2):104-114. doi:10.33434/cams.1242905
Chicago
Karahan, Döne, and Ecem Acar. 2023. “Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind”. Communications in Advanced Mathematical Sciences 6 (2): 104-14. https://doi.org/10.33434/cams.1242905.
EndNote
Karahan D, Acar E (June 1, 2023) Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences 6 2 104–114.
IEEE
[1]D. Karahan and E. Acar, “Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind”, Communications in Advanced Mathematical Sciences, vol. 6, no. 2, pp. 104–114, June 2023, doi: 10.33434/cams.1242905.
ISNAD
Karahan, Döne - Acar, Ecem. “Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind”. Communications in Advanced Mathematical Sciences 6/2 (June 1, 2023): 104-114. https://doi.org/10.33434/cams.1242905.
JAMA
1.Karahan D, Acar E. Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences. 2023;6:104–114.
MLA
Karahan, Döne, and Ecem Acar. “Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind”. Communications in Advanced Mathematical Sciences, vol. 6, no. 2, June 2023, pp. 104-1, doi:10.33434/cams.1242905.
Vancouver
1.Döne Karahan, Ecem Acar. Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences. 2023 Jun. 1;6(2):104-1. doi:10.33434/cams.1242905