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Yıl 2021, Cilt: 9 Sayı: 1, 9 - 21, 01.03.2021

Gumrah Uysal Başar Yılmaz

https://doi.org/10.36753/mathenot.763854
Cited By: 1

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

Gumrah Uysal Başar Yılmaz

https://doi.org/10.36753/mathenot.763854
Cited By: 1

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.

Anahtar Kelimeler

Fatou-type convergence Approximation of partial derivatives Integral operators

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).
Toplam 24 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Gumrah Uysal 0000-0001-7747-1706

Başar Yılmaz 0000-0003-3937-992X

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

Kaynak Göster

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. 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. Mart 2021;9(1):9-21. doi:10.36753/mathenot.763854
Chicago Uysal, Gumrah, ve Başar Yılmaz. “On Convergence of Partial Derivatives of Multidimensional Convolution Operators”. Mathematical Sciences and Applications E-Notes 9, sy. 1 (Mart 2021): 9-21. https://doi.org/10.36753/mathenot.763854.
EndNote Uysal G, Yılmaz B (01 Mart 2021) On Convergence of Partial Derivatives of Multidimensional Convolution Operators. Mathematical Sciences and Applications E-Notes 9 1 9–21.
IEEE G. Uysal ve B. Yılmaz, “On Convergence of Partial Derivatives of Multidimensional Convolution Operators”, Math. Sci. Appl. E-Notes, c. 9, sy. 1, ss. 9–21, 2021, doi: 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.
JAMA Uysal G, Yılmaz B. On Convergence of Partial Derivatives of Multidimensional Convolution Operators. Math. Sci. Appl. E-Notes. 2021;9:9–21.
MLA Uysal, Gumrah ve Başar Yılmaz. “On Convergence of Partial Derivatives of Multidimensional Convolution Operators”. Mathematical Sciences and Applications E-Notes, c. 9, sy. 1, 2021, ss. 9-21, doi:10.36753/mathenot.763854.
Vancouver Uysal G, Yılmaz B. On Convergence of Partial Derivatives of Multidimensional Convolution Operators. Math. Sci. Appl. E-Notes. 2021;9(1):9-21.

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