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CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS

Year 2015, Volume: 64 Issue: 1, 75 - 86, 01.02.2015
https://doi.org/10.1501/Commua1_0000000728

References

  • L. Angeloni and G. Vinti, Convergence and rate of approximation for linear integral operators in BV'-spaces in multidimensional setting, J. Math. Anal.and Appl., Vol. 349, (2009), 317
  • C. Bardaro, H. Karsli and G. Vinti, Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems, Appl. Anal., Vol. 90, Nos. 3–4, March–April (2011), 463–
  • C. Bardaro, H. Karsli and G. Vinti, On pointwise convergence of linear integral operators with homogeneous kernels , Integral Transforms and Special Functions, 19(6), (2008), 429-439.
  • C. Bardaro, I. Mantellini, Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math. 27(4) (2006), 431-447.
  • C. Bardaro, J. Musielak and G. Vinti , Nonlinear integral operators and applications, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 9, xii + 201 pp., 2003.
  • C. Bardaro, S. Sciamannini, G. Vinti, Convergence in BV'by nonlinear Mellin-type convo- lution operators, Func. et Approx., 29, (2001), 17-28.
  • S. N. Bernstein, Demonstration du Th¼eoreme de Weierstrass fond¼ee sur le calcul des proba- bilit¼es, Comm. Soc. Math. Kharkow 13, (1912/13), 1-2.
  • P.L. Butzer and R.J. Nessel, Fourier Analysis and Approximation, V.1, Academic Press, New York, London, 1971.
  • H. Karsli, Convergence and rate of convergence by nonlinear singular integral operators de- pending on two parameters, Appl. Anal. 85(6,7), (2006), 781-791.
  • H. Karsli, On approximation properties of a class of convolution type nonlinear singular integral operators , Georgian Math. Jour., Vol. 15, No. 1, (2008), 77–86.
  • H. Karsli, Some convergence results for nonlinear singular integral operators, Demonstratio. Math., Vol. XLVI No 4, 729-740 (2013).
  • H. Karsli and V. Gupta, Rate of convergence by nonlinear integral operators for functions of bounded variation, Calcolo, Vol. 45, 2, (2008), 87-99.
  • H. Karsli, I. U. Tiryaki, H. E. Altin, Some approximation properties of a certain nonlinear Bernstein operators, Filomat, 28(2014), 1295-1305.
  • G.G. Lorentz, Bernstein Polynomials, University of Toronto Press,Toronto (1953).
  • J. Musielak, On some approximation problems in modular spaces, In Constructive Function Theory 1981, (Proc. Int. Conf., Varna, June 1-5, 1981), pp. 455-461, Publ. House Bulgarian Acad. Sci., So…a 1983.
  • S.Y. Shaw, W.C. Liaw and Y.L. Lin, Rates for approximation of functions in BV [a; b] and DBV [a; b]by positive linear operators, Chinese J. Math. Vol 21., No: 2, (1993), 171-193.
Year 2015, Volume: 64 Issue: 1, 75 - 86, 01.02.2015
https://doi.org/10.1501/Commua1_0000000728

References

  • L. Angeloni and G. Vinti, Convergence and rate of approximation for linear integral operators in BV'-spaces in multidimensional setting, J. Math. Anal.and Appl., Vol. 349, (2009), 317
  • C. Bardaro, H. Karsli and G. Vinti, Nonlinear integral operators with homogeneous kernels: pointwise approximation theorems, Appl. Anal., Vol. 90, Nos. 3–4, March–April (2011), 463–
  • C. Bardaro, H. Karsli and G. Vinti, On pointwise convergence of linear integral operators with homogeneous kernels , Integral Transforms and Special Functions, 19(6), (2008), 429-439.
  • C. Bardaro, I. Mantellini, Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math. 27(4) (2006), 431-447.
  • C. Bardaro, J. Musielak and G. Vinti , Nonlinear integral operators and applications, De Gruyter Series in Nonlinear Analysis and Applications, Vol. 9, xii + 201 pp., 2003.
  • C. Bardaro, S. Sciamannini, G. Vinti, Convergence in BV'by nonlinear Mellin-type convo- lution operators, Func. et Approx., 29, (2001), 17-28.
  • S. N. Bernstein, Demonstration du Th¼eoreme de Weierstrass fond¼ee sur le calcul des proba- bilit¼es, Comm. Soc. Math. Kharkow 13, (1912/13), 1-2.
  • P.L. Butzer and R.J. Nessel, Fourier Analysis and Approximation, V.1, Academic Press, New York, London, 1971.
  • H. Karsli, Convergence and rate of convergence by nonlinear singular integral operators de- pending on two parameters, Appl. Anal. 85(6,7), (2006), 781-791.
  • H. Karsli, On approximation properties of a class of convolution type nonlinear singular integral operators , Georgian Math. Jour., Vol. 15, No. 1, (2008), 77–86.
  • H. Karsli, Some convergence results for nonlinear singular integral operators, Demonstratio. Math., Vol. XLVI No 4, 729-740 (2013).
  • H. Karsli and V. Gupta, Rate of convergence by nonlinear integral operators for functions of bounded variation, Calcolo, Vol. 45, 2, (2008), 87-99.
  • H. Karsli, I. U. Tiryaki, H. E. Altin, Some approximation properties of a certain nonlinear Bernstein operators, Filomat, 28(2014), 1295-1305.
  • G.G. Lorentz, Bernstein Polynomials, University of Toronto Press,Toronto (1953).
  • J. Musielak, On some approximation problems in modular spaces, In Constructive Function Theory 1981, (Proc. Int. Conf., Varna, June 1-5, 1981), pp. 455-461, Publ. House Bulgarian Acad. Sci., So…a 1983.
  • S.Y. Shaw, W.C. Liaw and Y.L. Lin, Rates for approximation of functions in BV [a; b] and DBV [a; b]by positive linear operators, Chinese J. Math. Vol 21., No: 2, (1993), 171-193.
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Details

Primary Language English
Journal Section Research Articles
Authors

Harun Karslı This is me

Erhan Altın H. This is me

Publication Date February 1, 2015
Published in Issue Year 2015 Volume: 64 Issue: 1

Cite

APA Karslı, H., & Altın H., E. (2015). CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 64(1), 75-86. https://doi.org/10.1501/Commua1_0000000728
AMA Karslı H, Altın H. E. CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. February 2015;64(1):75-86. doi:10.1501/Commua1_0000000728
Chicago Karslı, Harun, and Erhan Altın H. “CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64, no. 1 (February 2015): 75-86. https://doi.org/10.1501/Commua1_0000000728.
EndNote Karslı H, Altın H. E (February 1, 2015) CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64 1 75–86.
IEEE H. Karslı and E. Altın H., “CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 64, no. 1, pp. 75–86, 2015, doi: 10.1501/Commua1_0000000728.
ISNAD Karslı, Harun - Altın H., Erhan. “CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 64/1 (February 2015), 75-86. https://doi.org/10.1501/Commua1_0000000728.
JAMA Karslı H, Altın H. E. CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64:75–86.
MLA Karslı, Harun and Erhan Altın H. “CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 64, no. 1, 2015, pp. 75-86, doi:10.1501/Commua1_0000000728.
Vancouver Karslı H, Altın H. E. CONVERGENCE OF CERTAIN NONLINEAR COUNTERPART OF THE BERNSTEIN OPERATORS. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2015;64(1):75-86.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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