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Year 2023, Volume: 6 Issue: 2, 104 - 114, 30.06.2023
https://doi.org/10.33434/cams.1242905

Abstract

References

  • [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] G.M. Philips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.
  • [3] S. Ostrovska, q-Bernstein polynomials and their iterates, J. Approximation Theory, 123(2) (2003), 232-255.
  • [4] S. Ostrovska, On the Lupas q-analogue of the Bernstein operator, Rocky Mountain. J. Math., 36(5) (1997), 1615-1629.
  • [5] H. Oruc, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory, 117 (2002), 301-313.
  • [6] M.A. Siddigue, R.R. Aqrawal, N. Gupta, On a class of new Bernstein operators, Advanced Studies in Contemporary Mathematics, 2015.
  • [7] D. Karahan, A. Izgi, On approximation properties of generalized q-Bernstein operators, Num. Funct. Anal. Opt., 39 (2018), 990-998.
  • [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] B. Bede, L. Coroianu, S.G. Gal, Approximation by max-product type operators, Springer International Publishing Switzerland, 2016.
  • [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.
  • [11] B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the Bernstein operator of max-product kind, Int. J. Math Sci. Art. ID 590589, (2009), 26pp.
  • [12] B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Favard-Szasz-Mirakjan operator of max-product kind, Filomat, 24(3) (2010), 55-72.
  • [13] B. Bede, S.G. Gal, Approximation by nonlinear Bernstein and Favard-Sz´asz-Mirakyan operators of max-product kind, J. Concrete and Applicable Math., 8(2) (2010), 193–207.
  • [14] O. Duman, Nonlinear Approximation: q-Bernstein operators of max-product kind, Intelligent Mathematics II: Applied Mathematics and Approximation Theory, vol 441. Springer.
  • [15] J. Favard, Sur les multiplicateurs d’interpolation, J. Math. Pures Appl. Ser., 9(23) (1944), 219–247.
  • [16] N.I. Mahmudov, Approximation by the q-Szasz-Mirakjan operators, Abstr. Appl. Anal., 2012, Article ID 754217, 16 pages, 2012.
  • [17] G.H. Hardy, Divergent Series, Clarendon Press, Oxford, 1949.
  • [18] H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241-244.

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

Year 2023, Volume: 6 Issue: 2, 104 - 114, 30.06.2023
https://doi.org/10.33434/cams.1242905

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.

References

  • [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] G.M. Philips, Bernstein polynomials based on the q-integers, Ann. Numer. Math., 4 (1997), 511-518.
  • [3] S. Ostrovska, q-Bernstein polynomials and their iterates, J. Approximation Theory, 123(2) (2003), 232-255.
  • [4] S. Ostrovska, On the Lupas q-analogue of the Bernstein operator, Rocky Mountain. J. Math., 36(5) (1997), 1615-1629.
  • [5] H. Oruc, N. Tuncer, On the convergence and iterates of q-Bernstein polynomials, J. Approx. Theory, 117 (2002), 301-313.
  • [6] M.A. Siddigue, R.R. Aqrawal, N. Gupta, On a class of new Bernstein operators, Advanced Studies in Contemporary Mathematics, 2015.
  • [7] D. Karahan, A. Izgi, On approximation properties of generalized q-Bernstein operators, Num. Funct. Anal. Opt., 39 (2018), 990-998.
  • [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] B. Bede, L. Coroianu, S.G. Gal, Approximation by max-product type operators, Springer International Publishing Switzerland, 2016.
  • [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.
  • [11] B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the Bernstein operator of max-product kind, Int. J. Math Sci. Art. ID 590589, (2009), 26pp.
  • [12] B. Bede, L. Coroianu, S.G. Gal, Approximation and shape preserving properties of the nonlinear Favard-Szasz-Mirakjan operator of max-product kind, Filomat, 24(3) (2010), 55-72.
  • [13] B. Bede, S.G. Gal, Approximation by nonlinear Bernstein and Favard-Sz´asz-Mirakyan operators of max-product kind, J. Concrete and Applicable Math., 8(2) (2010), 193–207.
  • [14] O. Duman, Nonlinear Approximation: q-Bernstein operators of max-product kind, Intelligent Mathematics II: Applied Mathematics and Approximation Theory, vol 441. Springer.
  • [15] J. Favard, Sur les multiplicateurs d’interpolation, J. Math. Pures Appl. Ser., 9(23) (1944), 219–247.
  • [16] N.I. Mahmudov, Approximation by the q-Szasz-Mirakjan operators, Abstr. Appl. Anal., 2012, Article ID 754217, 16 pages, 2012.
  • [17] G.H. Hardy, Divergent Series, Clarendon Press, Oxford, 1949.
  • [18] H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241-244.
There are 18 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Döne Karahan 0000-0001-6644-5596

Ecem Acar 0000-0002-2517-5849

Publication Date June 30, 2023
Submission Date January 26, 2023
Acceptance Date June 28, 2023
Published in Issue Year 2023 Volume: 6 Issue: 2

Cite

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 Karahan D, Acar E. Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind. Communications in Advanced Mathematical Sciences. June 2023;6(2):104-114. doi:10.33434/cams.1242905
Chicago Karahan, Döne, and Ecem Acar. “Nonlinear Approximation by $q$-Favard-Sz{\’a}sz-Mirakjan Operators of Max-Product Kind”. Communications in Advanced Mathematical Sciences 6, no. 2 (June 2023): 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 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, 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 2023), 104-114. https://doi.org/10.33434/cams.1242905.
JAMA 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, 2023, pp. 104-1, doi:10.33434/cams.1242905.
Vancouver 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):104-1.

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