Araştırma Makalesi
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Yıl 2021, Cilt: 9 Sayı: 1, 9 - 21, 01.03.2021
https://doi.org/10.36753/mathenot.763854

Öz

Kaynakça

  • [1] Almali, S.E., Gadjiev, A.D.: On approximation properties of certain multidimensional nonlinear integrals. J. Nonlinear Sci. Appl. 9 (5) 3090–3097 (2016).
  • [2] Bardaro, C., Mantellini, I.: Voronovskaya-type estimates for Mellin convolution operators. Results Math. 50 (1-2) 1–16 (2007).
  • [3] Bardaro, C., Mantellini, I.: Bivariate Mellin convolution operators: Quantitative approximation theorems. Math. Comput. Modelling 53 (5-6) 1197–1207 (2011).
  • [4] Butzer, P.L., Nessel, R.J.: Fourier analysis and approximation Vol. 1: One-dimensional theory. Pure and Applied Mathematics Vol. 40. Academic Press: New York-London (1971).
  • [5] Fatou, P.: Séries trigonométriques et séries de Taylor (French). Acta Math. 30 (1) 335–400 (1906).
  • [6] Gadžiev, A.D.: The asymptotic value of the approximation of derivatives by the derivatives of a family of linear operators (Russian). Izv. Akad. Nauk Azerba˘ıdžan. SSR Ser. Fiz.-Mat. Tehn. Nauk 6 15–24 (1962).
  • [7] Gadžiev, A.D.: On the convergence of integral operators (Russian). Akad. Nauk Azerba˘ıdžan. SSR Dokl. 19 (12) 3–7 (1963).
  • [8] Gadžiev, A.D.: On the speed of convergence of a class of singular integrals (Russian). Izv. Akad. Nauk Azerbaıdžan. SSR Ser. Fiz.-Mat. Tehn. Nauk 6, 27–31 (1963).
  • [9] Gadžiev, A.D.: The order of convergence of singular integrals which depend on two parameters (Russian). In: Special problems of functional analysis and their applications to the theory of differential equations and the theory of functions (Russian), 40-44 (1968).
  • [10] Karsli, H., Ibikli, E.: Approximation properties of convolution type singular integral operators depending on two parameters and of their derivatives in L1(a; b). In: Proceedings of the 16th International Conference of the Jangjeon Mathematical Society, 66–76, Jangjeon Math. Soc.: Hapcheon (2005).
  • [11] Karsli, H.: Approximation properties of singular integrals depending on two parameters and their derivatives (Turkish). PhD Thesis, Ankara University, Ankara, 75 pp. (2006).
  • [12] Karsli, H.: Convergence of the derivatives of nonlinear singular integral operators. J. Math. Anal. Approx. Theory 2 (1) 26–34 (2007).
  • [13] Matsuoka, Y.: Asymptotic formula for Vallée Poussin’s singular integrals. Sci. Rep. Kagoshima Univ. 9, 25–34 (1960).
  • [14] Saks, S.: Theory of the integral. Monografie Matematyczne,Warszawa (1937).
  • [15] Siudut, S.: On the convergence of double singular integrals. Comment. Math. Prace Mat. 28 (1) 143–146 (1988).
  • [16] Siudut, S.: On the Fatou type convergence of abstract singular integrals. Comment. Math. Prace Mat. 30 (1) 171–176 (1990).
  • [17] Spivak, M.D.: Calculus. (3rd ed.), Publish or Perish, Incorporated: Houston-Texas (1994).
  • [18] Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30. Princeton Univ. Press: Princeton-New Jersey (1970).
  • [19] Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton Univ. Press: Princeton-New Jersey (1971).
  • [20] Taberski, R.: Singular integrals depending on two parameters. Prace Mat. 7, 173–179 (1962).
  • [21] Taberski, R.: On double integrals and Fourier series. Ann. Polon. Math. 15, 97–115 (1964).
  • [22] Uysal, G., Yilmaz, M.M., Ibikli, E.: Approximation by radial type multidimensional singular integral operators. Palest. J. Math. 5 (2) 61–70 (2016).
  • [23] Yilmaz, B., Aral, A., Tunca, G.B.: Weighted approximation properties of generalized Picard operators. J. Comput. Anal. Appl. 13 (3) 499–513 (2011).
  • [24] Žornickaja, L.V.: The derivatives of some singular integrals (Russian). Izv. Vysš. Uˇcebn. Zaved. Matematika 29 (4) 62–72 (1962).

On Convergence of Partial Derivatives of Multidimensional Convolution Operators

Yıl 2021, Cilt: 9 Sayı: 1, 9 - 21, 01.03.2021
https://doi.org/10.36753/mathenot.763854

Öz

In this paper, we prove some results on convergence properties of higher order partial derivatives of multidimensional convolution-type singular integral operators being applied to the class of functions which are integrable in the sense of Lebesgue.

Kaynakça

  • [1] Almali, S.E., Gadjiev, A.D.: On approximation properties of certain multidimensional nonlinear integrals. J. Nonlinear Sci. Appl. 9 (5) 3090–3097 (2016).
  • [2] Bardaro, C., Mantellini, I.: Voronovskaya-type estimates for Mellin convolution operators. Results Math. 50 (1-2) 1–16 (2007).
  • [3] Bardaro, C., Mantellini, I.: Bivariate Mellin convolution operators: Quantitative approximation theorems. Math. Comput. Modelling 53 (5-6) 1197–1207 (2011).
  • [4] Butzer, P.L., Nessel, R.J.: Fourier analysis and approximation Vol. 1: One-dimensional theory. Pure and Applied Mathematics Vol. 40. Academic Press: New York-London (1971).
  • [5] Fatou, P.: Séries trigonométriques et séries de Taylor (French). Acta Math. 30 (1) 335–400 (1906).
  • [6] Gadžiev, A.D.: The asymptotic value of the approximation of derivatives by the derivatives of a family of linear operators (Russian). Izv. Akad. Nauk Azerba˘ıdžan. SSR Ser. Fiz.-Mat. Tehn. Nauk 6 15–24 (1962).
  • [7] Gadžiev, A.D.: On the convergence of integral operators (Russian). Akad. Nauk Azerba˘ıdžan. SSR Dokl. 19 (12) 3–7 (1963).
  • [8] Gadžiev, A.D.: On the speed of convergence of a class of singular integrals (Russian). Izv. Akad. Nauk Azerbaıdžan. SSR Ser. Fiz.-Mat. Tehn. Nauk 6, 27–31 (1963).
  • [9] Gadžiev, A.D.: The order of convergence of singular integrals which depend on two parameters (Russian). In: Special problems of functional analysis and their applications to the theory of differential equations and the theory of functions (Russian), 40-44 (1968).
  • [10] Karsli, H., Ibikli, E.: Approximation properties of convolution type singular integral operators depending on two parameters and of their derivatives in L1(a; b). In: Proceedings of the 16th International Conference of the Jangjeon Mathematical Society, 66–76, Jangjeon Math. Soc.: Hapcheon (2005).
  • [11] Karsli, H.: Approximation properties of singular integrals depending on two parameters and their derivatives (Turkish). PhD Thesis, Ankara University, Ankara, 75 pp. (2006).
  • [12] Karsli, H.: Convergence of the derivatives of nonlinear singular integral operators. J. Math. Anal. Approx. Theory 2 (1) 26–34 (2007).
  • [13] Matsuoka, Y.: Asymptotic formula for Vallée Poussin’s singular integrals. Sci. Rep. Kagoshima Univ. 9, 25–34 (1960).
  • [14] Saks, S.: Theory of the integral. Monografie Matematyczne,Warszawa (1937).
  • [15] Siudut, S.: On the convergence of double singular integrals. Comment. Math. Prace Mat. 28 (1) 143–146 (1988).
  • [16] Siudut, S.: On the Fatou type convergence of abstract singular integrals. Comment. Math. Prace Mat. 30 (1) 171–176 (1990).
  • [17] Spivak, M.D.: Calculus. (3rd ed.), Publish or Perish, Incorporated: Houston-Texas (1994).
  • [18] Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30. Princeton Univ. Press: Princeton-New Jersey (1970).
  • [19] Stein, E.M., Weiss, G.: Introduction to Fourier analysis on Euclidean spaces. Princeton Mathematical Series, No. 32. Princeton Univ. Press: Princeton-New Jersey (1971).
  • [20] Taberski, R.: Singular integrals depending on two parameters. Prace Mat. 7, 173–179 (1962).
  • [21] Taberski, R.: On double integrals and Fourier series. Ann. Polon. Math. 15, 97–115 (1964).
  • [22] Uysal, G., Yilmaz, M.M., Ibikli, E.: Approximation by radial type multidimensional singular integral operators. Palest. J. Math. 5 (2) 61–70 (2016).
  • [23] Yilmaz, B., Aral, A., Tunca, G.B.: Weighted approximation properties of generalized Picard operators. J. Comput. Anal. Appl. 13 (3) 499–513 (2011).
  • [24] Žornickaja, L.V.: The derivatives of some singular integrals (Russian). Izv. Vysš. Uˇcebn. Zaved. Matematika 29 (4) 62–72 (1962).

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Gumrah UYSAL
KARABUK UNIVERSITY
0000-0001-7747-1706
Türkiye


Başar YILMAZ
Dr., Kırıkkale University,
0000-0003-3937-992X
Türkiye

Yayımlanma Tarihi 1 Mart 2021
Gönderilme Tarihi 3 Temmuz 2020
Kabul Tarihi 4 Aralık 2020
Yayınlandığı Sayı Yıl 2021 Cilt: 9 Sayı: 1

Kaynak Göster

Bibtex @araştırma makalesi { mathenot763854, journal = {Mathematical Sciences and Applications E-Notes}, eissn = {2147-6268}, address = {}, publisher = {Murat TOSUN}, year = {2021}, volume = {9}, number = {1}, pages = {9 - 21}, doi = {10.36753/mathenot.763854}, title = {On Convergence of Partial Derivatives of Multidimensional Convolution Operators}, key = {cite}, author = {Uysal, Gumrah and Yılmaz, Başar} }
APA Uysal, G. & Yılmaz, B. (2021). On Convergence of Partial Derivatives of Multidimensional Convolution Operators . Mathematical Sciences and Applications E-Notes , 9 (1) , 9-21 . DOI: 10.36753/mathenot.763854
MLA Uysal, G. , Yılmaz, B. "On Convergence of Partial Derivatives of Multidimensional Convolution Operators" . Mathematical Sciences and Applications E-Notes 9 (2021 ): 9-21 <https://dergipark.org.tr/tr/pub/mathenot/issue/60389/763854>
Chicago Uysal, G. , Yılmaz, B. "On Convergence of Partial Derivatives of Multidimensional Convolution Operators". Mathematical Sciences and Applications E-Notes 9 (2021 ): 9-21
RIS TY - JOUR T1 - On Convergence of Partial Derivatives of Multidimensional Convolution Operators AU - GumrahUysal, BaşarYılmaz Y1 - 2021 PY - 2021 N1 - doi: 10.36753/mathenot.763854 DO - 10.36753/mathenot.763854 T2 - Mathematical Sciences and Applications E-Notes JF - Journal JO - JOR SP - 9 EP - 21 VL - 9 IS - 1 SN - -2147-6268 M3 - doi: 10.36753/mathenot.763854 UR - https://doi.org/10.36753/mathenot.763854 Y2 - 2020 ER -
EndNote %0 Mathematical Sciences and Applications E-Notes On Convergence of Partial Derivatives of Multidimensional Convolution Operators %A Gumrah Uysal , Başar Yılmaz %T On Convergence of Partial Derivatives of Multidimensional Convolution Operators %D 2021 %J Mathematical Sciences and Applications E-Notes %P -2147-6268 %V 9 %N 1 %R doi: 10.36753/mathenot.763854 %U 10.36753/mathenot.763854
ISNAD Uysal, Gumrah , Yılmaz, Başar . "On Convergence of Partial Derivatives of Multidimensional Convolution Operators". Mathematical Sciences and Applications E-Notes 9 / 1 (Mart 2021): 9-21 . https://doi.org/10.36753/mathenot.763854
AMA Uysal G. , Yılmaz B. On Convergence of Partial Derivatives of Multidimensional Convolution Operators. Math. Sci. Appl. E-Notes. 2021; 9(1): 9-21.
Vancouver Uysal G. , Yılmaz B. On Convergence of Partial Derivatives of Multidimensional Convolution Operators. Mathematical Sciences and Applications E-Notes. 2021; 9(1): 9-21.
IEEE G. Uysal ve B. Yılmaz , "On Convergence of Partial Derivatives of Multidimensional Convolution Operators", Mathematical Sciences and Applications E-Notes, c. 9, sayı. 1, ss. 9-21, Mar. 2021, doi:10.36753/mathenot.763854

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