Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2018, Cilt: 1 Sayı: 2, 113 - 127, 07.11.2018
https://doi.org/10.33205/cma.478408

Öz

Kaynakça

  • [1] U. Abel, M. Ivan, Asymptotic expansion of the multivariate Bernstein polynomials on a simplex, Approx. Theory Appl. 16 (2000), 85-93.
  • [2] A. M. Acu, I. Raşa, New estimates for the differences of positive linear operators, Numerical Algorithms 73(3) (2016), 775-789.
  • [3] A. M. Acu, I. Raşa, Estimates for the differences of positive linear operators and their derivatives, arXiv:1810.08839v1, submitted.
  • [4] A. Aral, D. Inoan and I. Raşa, On differences of linear positive operators, Anal. Math. Phys.(2018). DOI https://doi.org/10.1007/s1332
  • [5] S. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Communications de la Société Mathematique de Kharkov, 13 (1913), 1-2.
  • [6] W. Chen, On the modified Bernstein-Durrmeyer operator, Report of the Fifth Chinese Conference on Approximation Theory, Zhen Zhou, China, 1987.
  • [7] H. Gonska, I. Ra¸sa, E.-D. Stanila, Beta operators with Jacobi weights, In: Constructive theory of functions, Sozopol 2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), 99–112. Prof. Marin Drinov Academic Publishing House, Sofia, 2014.
  • [8] H. Gonska, I. Raşa, Differences of positive linear operators and the second order modulus, Carpathian J. Math. 24(3) (2008), 332-340.
  • [9] H. Gonska, P. Pitul, I. Ra¸sa, On differences of positive linear operators, Carpathian J. Math. 22(1-2) (2006), 65-78.
  • [10] H. Gonska, P. Pitul, I. Ra¸sa, On Peano’s form of the Taylor remainder, Voronovskaja’s theorem and the commutator of positive linear operators, in Numerical Analysis and Approximation Theory (Proc. Int. Conf. Cluj-Napoca 2006; ed. by O. Agratini and P. Blaga), Cluj-Napoca, Casa C˘ar¸tii de ¸Stiin¸ta, 2006, 55-80.
  • [11] H. Gonska, R. Paltanea, Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions, Czechoslovak Math. J. 60(135) (2010), 783-799.
  • [12] H. Gonska, R. Paltanea, Quantitative convergence theorems for a class of Bernstein-Durrmeyer operators preserving linear functions, Ukrainian Math. J. 62 (2010), 913-922.
  • [13] T. N. T. Goodman, A. Sharma, A modified Bernstein-Schoenberg operator, Proc. of the Conference on Constructive Theory of Functions, Varna 1987 (ed. by Bl. Sendov et al.). Sofia: Publ. House Bulg. Acad. of Sci., 1988, 166-173.
  • [14] M. Heilmann, F. Nasaireh, I. Ra¸sa, Complements to Voronovskaja’s formula, Chapter 11 In: D. Ghosh et al. (eds.), Mathematics and Computing, Springer Proceedings in Mathematics & Statistics 253, Springer Nature Singapore Pte Ltd. 2018, https://doi.org/10.1007/978-981-13-2095-8 11.
  • [15] M. Heilmann, F. Nasaireh, I. Ra¸sa, Discrete Operators associated with Linking Operators, arXiv:1808.07239v1.
  • [16] N. Ispir, On modified Baskakov operators on weighted spaces Turk. J. Math. 26(3) (2001), 355-365.
  • [17] L.V. Kantorovich, Sur certain développements suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. URSS 563-568 (1930), 595-600.
  • [18] A. Lupaş, The approximation by means of some linear positive operators, in Approximation Theory (M.W. Müller et al., eds), Akademie-Verlag, Berlin, 1995, 201-227.
  • [19] A. Lupaş, Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart, 1972.
  • [20] L. Lupaş, A. Lupa¸s, Polynomials of Binomial Type and Approximation Operators, Studia Univ. Babe¸s-Bolyai, Mathematica, XXXII, 4 (1987), 61-70.
  • [21] D.H. Mache, Gewichtete Simultanapproximation in der Lp-Metrik durch das Verfahren der Kantorovic Operatoren, Dissertation, Univ. Dortmund, 1991.
  • [22] D.H. Mache, A link between Bernstein polynomials and Durrmeyer polynomials with Jacobi weights, In: Approx. Theory VIII, Vol. 1: Approximation and Interpolation, Ch.K. Chui and L.L. Schmaker (Eds.), 403-410, World Scientific Publ., 1995.
  • [23] S.M. Mazhar, V. Totik, Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257-269.
  • [24] F. Nasaireh, I. Ra¸sa, Another look at Voronovskaya type formulas, Journal of Mathematical Inequalities, 12(1) (2018), 95-105.
  • [25] F. Nasaireh, Voronovskaja-type formulas and applications, General Mathematics, 25(1-2) (2017), 37-43.
  • [26] R. Paltanea, A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Sem. Funct. Equat. Approxim. Convex. (Cluj-Napoca) 5 (2007), 109-117.
  • [27] I. Raşa, Discrete operators associated with certain integral operators, Stud. Univ. Babe¸s- Bolyai Math., 56(2) (2011), 537-544.
  • [28] I. Raşa, E. Stanila, On some operators linking the Bernstein and the genuine Bernstein-Durrmeyer operators, J. Appl. Funct. Anal. 9 (2014), 369-378.
  • [29] D. D. Stancu, Asupra unei generalizari a polinoamelor lui Bernstein, Stud. Univ. Babes-Bolyai Math. 14 (1969), 31-45.
  • [30] E. D. Stanila, On Bernstein-Euler-Jacobi Operators, Ph D Thesis, Duisburg-Essen University, July, 2014.
  • [31] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval J. Res. Natl. Bur. Stand. 45 (1950), 239-245.

A Survey on Estimates for the Differences of Positive Linear Operators

Yıl 2018, Cilt: 1 Sayı: 2, 113 - 127, 07.11.2018
https://doi.org/10.33205/cma.478408

Öz

We survey some results concerning differences of positive linear operators from Approximation Theory, and present some new results in this direction.

Kaynakça

  • [1] U. Abel, M. Ivan, Asymptotic expansion of the multivariate Bernstein polynomials on a simplex, Approx. Theory Appl. 16 (2000), 85-93.
  • [2] A. M. Acu, I. Raşa, New estimates for the differences of positive linear operators, Numerical Algorithms 73(3) (2016), 775-789.
  • [3] A. M. Acu, I. Raşa, Estimates for the differences of positive linear operators and their derivatives, arXiv:1810.08839v1, submitted.
  • [4] A. Aral, D. Inoan and I. Raşa, On differences of linear positive operators, Anal. Math. Phys.(2018). DOI https://doi.org/10.1007/s1332
  • [5] S. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Communications de la Société Mathematique de Kharkov, 13 (1913), 1-2.
  • [6] W. Chen, On the modified Bernstein-Durrmeyer operator, Report of the Fifth Chinese Conference on Approximation Theory, Zhen Zhou, China, 1987.
  • [7] H. Gonska, I. Ra¸sa, E.-D. Stanila, Beta operators with Jacobi weights, In: Constructive theory of functions, Sozopol 2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), 99–112. Prof. Marin Drinov Academic Publishing House, Sofia, 2014.
  • [8] H. Gonska, I. Raşa, Differences of positive linear operators and the second order modulus, Carpathian J. Math. 24(3) (2008), 332-340.
  • [9] H. Gonska, P. Pitul, I. Ra¸sa, On differences of positive linear operators, Carpathian J. Math. 22(1-2) (2006), 65-78.
  • [10] H. Gonska, P. Pitul, I. Ra¸sa, On Peano’s form of the Taylor remainder, Voronovskaja’s theorem and the commutator of positive linear operators, in Numerical Analysis and Approximation Theory (Proc. Int. Conf. Cluj-Napoca 2006; ed. by O. Agratini and P. Blaga), Cluj-Napoca, Casa C˘ar¸tii de ¸Stiin¸ta, 2006, 55-80.
  • [11] H. Gonska, R. Paltanea, Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions, Czechoslovak Math. J. 60(135) (2010), 783-799.
  • [12] H. Gonska, R. Paltanea, Quantitative convergence theorems for a class of Bernstein-Durrmeyer operators preserving linear functions, Ukrainian Math. J. 62 (2010), 913-922.
  • [13] T. N. T. Goodman, A. Sharma, A modified Bernstein-Schoenberg operator, Proc. of the Conference on Constructive Theory of Functions, Varna 1987 (ed. by Bl. Sendov et al.). Sofia: Publ. House Bulg. Acad. of Sci., 1988, 166-173.
  • [14] M. Heilmann, F. Nasaireh, I. Ra¸sa, Complements to Voronovskaja’s formula, Chapter 11 In: D. Ghosh et al. (eds.), Mathematics and Computing, Springer Proceedings in Mathematics & Statistics 253, Springer Nature Singapore Pte Ltd. 2018, https://doi.org/10.1007/978-981-13-2095-8 11.
  • [15] M. Heilmann, F. Nasaireh, I. Ra¸sa, Discrete Operators associated with Linking Operators, arXiv:1808.07239v1.
  • [16] N. Ispir, On modified Baskakov operators on weighted spaces Turk. J. Math. 26(3) (2001), 355-365.
  • [17] L.V. Kantorovich, Sur certain développements suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. URSS 563-568 (1930), 595-600.
  • [18] A. Lupaş, The approximation by means of some linear positive operators, in Approximation Theory (M.W. Müller et al., eds), Akademie-Verlag, Berlin, 1995, 201-227.
  • [19] A. Lupaş, Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart, 1972.
  • [20] L. Lupaş, A. Lupa¸s, Polynomials of Binomial Type and Approximation Operators, Studia Univ. Babe¸s-Bolyai, Mathematica, XXXII, 4 (1987), 61-70.
  • [21] D.H. Mache, Gewichtete Simultanapproximation in der Lp-Metrik durch das Verfahren der Kantorovic Operatoren, Dissertation, Univ. Dortmund, 1991.
  • [22] D.H. Mache, A link between Bernstein polynomials and Durrmeyer polynomials with Jacobi weights, In: Approx. Theory VIII, Vol. 1: Approximation and Interpolation, Ch.K. Chui and L.L. Schmaker (Eds.), 403-410, World Scientific Publ., 1995.
  • [23] S.M. Mazhar, V. Totik, Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257-269.
  • [24] F. Nasaireh, I. Ra¸sa, Another look at Voronovskaya type formulas, Journal of Mathematical Inequalities, 12(1) (2018), 95-105.
  • [25] F. Nasaireh, Voronovskaja-type formulas and applications, General Mathematics, 25(1-2) (2017), 37-43.
  • [26] R. Paltanea, A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Sem. Funct. Equat. Approxim. Convex. (Cluj-Napoca) 5 (2007), 109-117.
  • [27] I. Raşa, Discrete operators associated with certain integral operators, Stud. Univ. Babe¸s- Bolyai Math., 56(2) (2011), 537-544.
  • [28] I. Raşa, E. Stanila, On some operators linking the Bernstein and the genuine Bernstein-Durrmeyer operators, J. Appl. Funct. Anal. 9 (2014), 369-378.
  • [29] D. D. Stancu, Asupra unei generalizari a polinoamelor lui Bernstein, Stud. Univ. Babes-Bolyai Math. 14 (1969), 31-45.
  • [30] E. D. Stanila, On Bernstein-Euler-Jacobi Operators, Ph D Thesis, Duisburg-Essen University, July, 2014.
  • [31] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval J. Res. Natl. Bur. Stand. 45 (1950), 239-245.
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Ana Maria Acu 0000-0003-1192-2281

Sever Hodış Bu kişi benim 0000-0003-1192-2281

Ioan Raşa Bu kişi benim 0000-0002-5206-030X

Yayımlanma Tarihi 7 Kasım 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 1 Sayı: 2

Kaynak Göster

APA Acu, A. M., Hodış, S., & Raşa, I. (2018). A Survey on Estimates for the Differences of Positive Linear Operators. Constructive Mathematical Analysis, 1(2), 113-127. https://doi.org/10.33205/cma.478408
AMA Acu AM, Hodış S, Raşa I. A Survey on Estimates for the Differences of Positive Linear Operators. CMA. Kasım 2018;1(2):113-127. doi:10.33205/cma.478408
Chicago Acu, Ana Maria, Sever Hodış, ve Ioan Raşa. “A Survey on Estimates for the Differences of Positive Linear Operators”. Constructive Mathematical Analysis 1, sy. 2 (Kasım 2018): 113-27. https://doi.org/10.33205/cma.478408.
EndNote Acu AM, Hodış S, Raşa I (01 Kasım 2018) A Survey on Estimates for the Differences of Positive Linear Operators. Constructive Mathematical Analysis 1 2 113–127.
IEEE A. M. Acu, S. Hodış, ve I. Raşa, “A Survey on Estimates for the Differences of Positive Linear Operators”, CMA, c. 1, sy. 2, ss. 113–127, 2018, doi: 10.33205/cma.478408.
ISNAD Acu, Ana Maria vd. “A Survey on Estimates for the Differences of Positive Linear Operators”. Constructive Mathematical Analysis 1/2 (Kasım 2018), 113-127. https://doi.org/10.33205/cma.478408.
JAMA Acu AM, Hodış S, Raşa I. A Survey on Estimates for the Differences of Positive Linear Operators. CMA. 2018;1:113–127.
MLA Acu, Ana Maria vd. “A Survey on Estimates for the Differences of Positive Linear Operators”. Constructive Mathematical Analysis, c. 1, sy. 2, 2018, ss. 113-27, doi:10.33205/cma.478408.
Vancouver Acu AM, Hodış S, Raşa I. A Survey on Estimates for the Differences of Positive Linear Operators. CMA. 2018;1(2):113-27.

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