Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2021, , 215 - 228, 01.06.2021
https://doi.org/10.33205/cma.862942

Öz

Kaynakça

  • T. Acar, A. Aral and I. Raşa: Modified Bernstein-Durrmeyer operators, Gen. Math., 22 (1) (2014), 27-41.
  • F. Altomare, M. Campiti: Korovkin-type approximation theory and its applications, Walter de Gruyter, Berlin-New York (1994).
  • A. Attalienti: Generalized Bernstein-Durrmeyer operators and the associated limit semigroup, J. Approx. Theory, 99 (1999), 289-309.
  • E. Berdysheva, K. Jetter: Multivariate Bernstein–Durrmeyer operators with arbitrary weight functions, J. Approx. Theory, 162 (2010), 576-598.
  • H. Berens, Y. Xu: On Bernstein-Durrmeyer polynomials with Jacobi weights, Approximation Theory and Functional Analysis, (College Station, TX, 1990), 25–46, Academic Press, Boston (1991).
  • W. Z. Chen: On the modified Bernstein-Durrmeyer operator, In Report of the Fifth Chinese Conference on Approximation Theory, Zhen Zhou, China (1987).
  • M. M. Derriennic: Sur l’approximation de fonctions intégrables sur [0, 1] par des polynômes de Bernstein modifies, J. Approx. Theory, 31 (1981), 325–343.
  • M. M. Derriennic: On multivariate approximation by Bernstein-type polynomials, J. Approx. Theory, 45 (2) (1985), 155–166.
  • Z. Ditzian: Multidimensional Jacobi-type Bernstein–Durrmeyer operators, Acta Sci. Math., (Szeged) 60 (1995), 225–243.
  • S. Durrmeyer: Une formule d’inversion de la transforme de Laplace: Application a la theorie de moments, Dissertation, These de 3e cycle, Faculté de Sci. de Univ. Paris, (1967).
  • I. Gavrea: The approximation of the continuous functions by means of some linear positive operators, Result. Math., 30 (1-2) (1996), 55-66.
  • H. Gonska, R. Pâltânea: Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions, Czech. Math. J., 60 (135) (2010), 783–799.
  • H. Gonska, I. Raşa and E.- D. Stânilâ: The eigenstructure of operators linking the Bernstein and the genuine BernsteinDurrmeyer operators, Mediterr. J. Math., 11 (2014), 561-576.
  • 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.
  • V. Gupta, G. Tachev: Approximation with positive linear operators and linear combinations, Springer, (2017).
  • B. Li: Approximation by a class of modified Bernstein-Durrmeyer operators, Approx. Th. Appl., 10 (1994), 32-44.
  • A. Lupa¸s: Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart (1972).
  • D. H. Mache, D.X. Zhou: Characterization theorems for the approximation by a family of operators, J. Approx. Theory, 84 (1996), 145–161.
  • P. E. Parvanov, B. D. Popov: The limit case of Bernstein’s operators with Jacobi weights, Math. Balkanica (N.S.), 8 (1994), 165–177.
  • R. Pâltânea: Sur un operateur polynômial défini sur l’ensemble des fonctions intégrables, Babes Bolyai Univ., Fac. Math., Res. Semin., 2 (1983), 101–106.
  • R. Pâlt3anea: Une propriété d’extrémalité des valeurs propres des opérateurs polynômiaux de Durrmeyer généralisés, L’Analyse Numér. et la Theor. de l’Approx., 15 (1986), 57–64.
  • R. Pâltânea: On a limit operator. Proc. of the "Tiberiu Popoviciu" Itinerant Seminar of Functional Equations, Approximation and Convexity, (ed. by E. Popoviciu), Srima Press, Cluj-Napoca (2001), 169-179.
  • R. Pâltânea: Approximation Theory Using Positive Linear Operators, Birkhäuser, Boston (2004).
  • R. Pâltânea: A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 5 (2007), 109–117.
  • R. Pâltânea: Generalized Bernstein-Durrmeyer operators on a simplex, Gen. Math., 20 (5) (2012), 71-82.
  • T. Sauer: The genuine Bernstein–Durrmeyer operator on a simplex, Results. Math., 26 (1–2) (1994), 99–130.
  • L. Song: Some approximation theorems for modified Bernstein-Durrmeyer operators, Approx. Th. Appl., 10 (1994), 1-12.
  • S. Waldron: A generalised beta integral and the limit of the Bernstein–Durrmeyer operator with Jacobi weights, J. Approx. Theory, 122 (2003), 141-150.

Durrmeyer type operators on a simplex

Yıl 2021, , 215 - 228, 01.06.2021
https://doi.org/10.33205/cma.862942

Öz

The paper contains the definition and certain approximation properties of a sequence of Durrmeyer-type operators on a simplex, which preserve affine functions and make a link between the multidimensional "genuine" Durrmeyer operators and the multidimensional Bernstein operators.

Kaynakça

  • T. Acar, A. Aral and I. Raşa: Modified Bernstein-Durrmeyer operators, Gen. Math., 22 (1) (2014), 27-41.
  • F. Altomare, M. Campiti: Korovkin-type approximation theory and its applications, Walter de Gruyter, Berlin-New York (1994).
  • A. Attalienti: Generalized Bernstein-Durrmeyer operators and the associated limit semigroup, J. Approx. Theory, 99 (1999), 289-309.
  • E. Berdysheva, K. Jetter: Multivariate Bernstein–Durrmeyer operators with arbitrary weight functions, J. Approx. Theory, 162 (2010), 576-598.
  • H. Berens, Y. Xu: On Bernstein-Durrmeyer polynomials with Jacobi weights, Approximation Theory and Functional Analysis, (College Station, TX, 1990), 25–46, Academic Press, Boston (1991).
  • W. Z. Chen: On the modified Bernstein-Durrmeyer operator, In Report of the Fifth Chinese Conference on Approximation Theory, Zhen Zhou, China (1987).
  • M. M. Derriennic: Sur l’approximation de fonctions intégrables sur [0, 1] par des polynômes de Bernstein modifies, J. Approx. Theory, 31 (1981), 325–343.
  • M. M. Derriennic: On multivariate approximation by Bernstein-type polynomials, J. Approx. Theory, 45 (2) (1985), 155–166.
  • Z. Ditzian: Multidimensional Jacobi-type Bernstein–Durrmeyer operators, Acta Sci. Math., (Szeged) 60 (1995), 225–243.
  • S. Durrmeyer: Une formule d’inversion de la transforme de Laplace: Application a la theorie de moments, Dissertation, These de 3e cycle, Faculté de Sci. de Univ. Paris, (1967).
  • I. Gavrea: The approximation of the continuous functions by means of some linear positive operators, Result. Math., 30 (1-2) (1996), 55-66.
  • H. Gonska, R. Pâltânea: Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions, Czech. Math. J., 60 (135) (2010), 783–799.
  • H. Gonska, I. Raşa and E.- D. Stânilâ: The eigenstructure of operators linking the Bernstein and the genuine BernsteinDurrmeyer operators, Mediterr. J. Math., 11 (2014), 561-576.
  • 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.
  • V. Gupta, G. Tachev: Approximation with positive linear operators and linear combinations, Springer, (2017).
  • B. Li: Approximation by a class of modified Bernstein-Durrmeyer operators, Approx. Th. Appl., 10 (1994), 32-44.
  • A. Lupa¸s: Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart (1972).
  • D. H. Mache, D.X. Zhou: Characterization theorems for the approximation by a family of operators, J. Approx. Theory, 84 (1996), 145–161.
  • P. E. Parvanov, B. D. Popov: The limit case of Bernstein’s operators with Jacobi weights, Math. Balkanica (N.S.), 8 (1994), 165–177.
  • R. Pâltânea: Sur un operateur polynômial défini sur l’ensemble des fonctions intégrables, Babes Bolyai Univ., Fac. Math., Res. Semin., 2 (1983), 101–106.
  • R. Pâlt3anea: Une propriété d’extrémalité des valeurs propres des opérateurs polynômiaux de Durrmeyer généralisés, L’Analyse Numér. et la Theor. de l’Approx., 15 (1986), 57–64.
  • R. Pâltânea: On a limit operator. Proc. of the "Tiberiu Popoviciu" Itinerant Seminar of Functional Equations, Approximation and Convexity, (ed. by E. Popoviciu), Srima Press, Cluj-Napoca (2001), 169-179.
  • R. Pâltânea: Approximation Theory Using Positive Linear Operators, Birkhäuser, Boston (2004).
  • R. Pâltânea: A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Semin. Funct. Equ. Approx. Convexity, 5 (2007), 109–117.
  • R. Pâltânea: Generalized Bernstein-Durrmeyer operators on a simplex, Gen. Math., 20 (5) (2012), 71-82.
  • T. Sauer: The genuine Bernstein–Durrmeyer operator on a simplex, Results. Math., 26 (1–2) (1994), 99–130.
  • L. Song: Some approximation theorems for modified Bernstein-Durrmeyer operators, Approx. Th. Appl., 10 (1994), 1-12.
  • S. Waldron: A generalised beta integral and the limit of the Bernstein–Durrmeyer operator with Jacobi weights, J. Approx. Theory, 122 (2003), 141-150.
Toplam 28 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Radu Paltanea 0000-0002-9923-4290

Yayımlanma Tarihi 1 Haziran 2021
Yayımlandığı Sayı Yıl 2021

Kaynak Göster

APA Paltanea, R. (2021). Durrmeyer type operators on a simplex. Constructive Mathematical Analysis, 4(2), 215-228. https://doi.org/10.33205/cma.862942
AMA Paltanea R. Durrmeyer type operators on a simplex. CMA. Haziran 2021;4(2):215-228. doi:10.33205/cma.862942
Chicago Paltanea, Radu. “Durrmeyer Type Operators on a Simplex”. Constructive Mathematical Analysis 4, sy. 2 (Haziran 2021): 215-28. https://doi.org/10.33205/cma.862942.
EndNote Paltanea R (01 Haziran 2021) Durrmeyer type operators on a simplex. Constructive Mathematical Analysis 4 2 215–228.
IEEE R. Paltanea, “Durrmeyer type operators on a simplex”, CMA, c. 4, sy. 2, ss. 215–228, 2021, doi: 10.33205/cma.862942.
ISNAD Paltanea, Radu. “Durrmeyer Type Operators on a Simplex”. Constructive Mathematical Analysis 4/2 (Haziran 2021), 215-228. https://doi.org/10.33205/cma.862942.
JAMA Paltanea R. Durrmeyer type operators on a simplex. CMA. 2021;4:215–228.
MLA Paltanea, Radu. “Durrmeyer Type Operators on a Simplex”. Constructive Mathematical Analysis, c. 4, sy. 2, 2021, ss. 215-28, doi:10.33205/cma.862942.
Vancouver Paltanea R. Durrmeyer type operators on a simplex. CMA. 2021;4(2):215-28.