Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 2 Sayı: 2, 81 - 88, 01.06.2019
https://doi.org/10.33205/cma.530987

Öz

Kaynakça

  • [1] T. Acar and S. A. Mohiuddine, Statistical (C; 1)(E; 1) Summability and Korovkin’s Theorem, Filomat, 30:02, 2016, 387–393.
  • [2] D. Cárdenas-Morales, P. Garrancho and I. Ra¸sa, Bernstein-type operators which preserve polynomials, Comput. Math. Appl., 62, 2011, 158–163.
  • [3] D. Cárdenas-Morales and P. Garrancho, B􀀀statistical A-summability in conservative approximation, Math. Inequal. Appl.,19(3), 2016, 923–936.
  • [4] O. Duman, M. K. Khan and C. Orhan, A-Statistical convergence of approximating operators, Math. Inequal. Appl. 6, 2003, 689–699.
  • [5] H. Fast, Sur la convergence statistique, Colloq. Math., 2, 1951, 241–244.
  • [6] A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32, 2002, 129–138.
  • [7] P. Garrancho and D. Cárdenas-Morales, A converse of asymptotic formulae in simultaneous approximation, Appl. Math. and Comp., 217, 2010, 2676–2683.
  • [8] A. Karaisa, Statistical $\alpha\beta$-Summability and Korovkin Type Approximation Theorem, Filomat ,30:13, 2016, 3483–3491.
  • [9] V. Karakaya and A. Karaisa, Korovkin type approximation theorems for weighted $\alpha\beta$-statistical convergence, Bull. Math. Sci., 5, 2015, 159–169.
  • [10] J. P. King and J. J. Swetits, Positive linear operators and summability, Austral J. Math., 11, 1970, 281–291.
  • [11] P. P. Korovkin, Linear operators and approximation theory, Hindustan Publishing Corp., Delhi, India, 1960.
  • [12] V. Loku and N. L. Braha, Tauberian Theorems by Weighted Summability Method, Armenian J. of Math., 9(1), 2017, 35–42.
  • [13] A.-J. López-Moreno and F.-J. Muñoz-Delgado, Asymptotic expansion of multivariate conservative linear operators, J. Comput. Appl. Math, 150, 2003, 219–251.
  • [14] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta. Math., 80, 1948, 167–190.
  • [15] H. Sharma, R. Maurya and C. Gupta, Approximation properties of Kantorovich Type Modifications of p; q-Meyer-König- Zeller Operators, Constr. Math. Anal., 1(1), 2018, 58–72.

A General Korovkin Result Under Generalized Convergence

Yıl 2019, Cilt: 2 Sayı: 2, 81 - 88, 01.06.2019
https://doi.org/10.33205/cma.530987

Öz

In this paper the classic result of Korovkin about the convergence of sequences of functions defined from sequences of linear operators is reformulated in terms of generalized convergence. This convergence extends some others given in the literature. The operator of the sequence fulfill a shape preserving property more general than the positivity. This property is related with certain extension of the notion of derivative. This extended derivative is precisely the object of the approximation process. The study is completed by analysing the conditions for the existence of an asymptotic formula, from which some interesting consequences are derived as a local version of the shape preserving property. Finally, as applications of the previous results, the author use the following notion of generalized convergence, an extension of Nörlund-Cesaro summability given by V. Loku and N. L. Braha in 2017. A way to transfer a notion of generalized convergence to approximation theory by means of linear operators is showed.

Kaynakça

  • [1] T. Acar and S. A. Mohiuddine, Statistical (C; 1)(E; 1) Summability and Korovkin’s Theorem, Filomat, 30:02, 2016, 387–393.
  • [2] D. Cárdenas-Morales, P. Garrancho and I. Ra¸sa, Bernstein-type operators which preserve polynomials, Comput. Math. Appl., 62, 2011, 158–163.
  • [3] D. Cárdenas-Morales and P. Garrancho, B􀀀statistical A-summability in conservative approximation, Math. Inequal. Appl.,19(3), 2016, 923–936.
  • [4] O. Duman, M. K. Khan and C. Orhan, A-Statistical convergence of approximating operators, Math. Inequal. Appl. 6, 2003, 689–699.
  • [5] H. Fast, Sur la convergence statistique, Colloq. Math., 2, 1951, 241–244.
  • [6] A. D. Gadjiev and C. Orhan, Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32, 2002, 129–138.
  • [7] P. Garrancho and D. Cárdenas-Morales, A converse of asymptotic formulae in simultaneous approximation, Appl. Math. and Comp., 217, 2010, 2676–2683.
  • [8] A. Karaisa, Statistical $\alpha\beta$-Summability and Korovkin Type Approximation Theorem, Filomat ,30:13, 2016, 3483–3491.
  • [9] V. Karakaya and A. Karaisa, Korovkin type approximation theorems for weighted $\alpha\beta$-statistical convergence, Bull. Math. Sci., 5, 2015, 159–169.
  • [10] J. P. King and J. J. Swetits, Positive linear operators and summability, Austral J. Math., 11, 1970, 281–291.
  • [11] P. P. Korovkin, Linear operators and approximation theory, Hindustan Publishing Corp., Delhi, India, 1960.
  • [12] V. Loku and N. L. Braha, Tauberian Theorems by Weighted Summability Method, Armenian J. of Math., 9(1), 2017, 35–42.
  • [13] A.-J. López-Moreno and F.-J. Muñoz-Delgado, Asymptotic expansion of multivariate conservative linear operators, J. Comput. Appl. Math, 150, 2003, 219–251.
  • [14] G. G. Lorentz, A contribution to the theory of divergent sequences, Acta. Math., 80, 1948, 167–190.
  • [15] H. Sharma, R. Maurya and C. Gupta, Approximation properties of Kantorovich Type Modifications of p; q-Meyer-König- Zeller Operators, Constr. Math. Anal., 1(1), 2018, 58–72.
Toplam 15 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Pedro Garrancho 0000-0002-7914-7843

Yayımlanma Tarihi 1 Haziran 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 2

Kaynak Göster

APA Garrancho, P. (2019). A General Korovkin Result Under Generalized Convergence. Constructive Mathematical Analysis, 2(2), 81-88. https://doi.org/10.33205/cma.530987
AMA Garrancho P. A General Korovkin Result Under Generalized Convergence. CMA. Haziran 2019;2(2):81-88. doi:10.33205/cma.530987
Chicago Garrancho, Pedro. “A General Korovkin Result Under Generalized Convergence”. Constructive Mathematical Analysis 2, sy. 2 (Haziran 2019): 81-88. https://doi.org/10.33205/cma.530987.
EndNote Garrancho P (01 Haziran 2019) A General Korovkin Result Under Generalized Convergence. Constructive Mathematical Analysis 2 2 81–88.
IEEE P. Garrancho, “A General Korovkin Result Under Generalized Convergence”, CMA, c. 2, sy. 2, ss. 81–88, 2019, doi: 10.33205/cma.530987.
ISNAD Garrancho, Pedro. “A General Korovkin Result Under Generalized Convergence”. Constructive Mathematical Analysis 2/2 (Haziran 2019), 81-88. https://doi.org/10.33205/cma.530987.
JAMA Garrancho P. A General Korovkin Result Under Generalized Convergence. CMA. 2019;2:81–88.
MLA Garrancho, Pedro. “A General Korovkin Result Under Generalized Convergence”. Constructive Mathematical Analysis, c. 2, sy. 2, 2019, ss. 81-88, doi:10.33205/cma.530987.
Vancouver Garrancho P. A General Korovkin Result Under Generalized Convergence. CMA. 2019;2(2):81-8.