BibTex RIS Kaynak Göster

NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE

Yıl 2018, Cilt: 67 Sayı: 1, 262 - 276, 01.02.2018
https://doi.org/10.1501/Commua1_0000000848

Öz

In the present paper, we prove some theorems concerning Fatoutype weighted pointwise convergence of nonlinear m singular integral operators of the form

Kaynakça

  • Alexits, G., Convergence problems of orthogonal series. Translated from the German by I. Földer, International Series of Monographs in Pure and Applied Mathematics vol. 20, Pergamon Press, New York (1961).
  • Bardaro, C., On approximation properties for some classes of linear operators of convolution type. Atti Sem. Mat. Fis. Univ. Modena, 33 (1984), 329-356.
  • Bardaro, C., Musielak, J. and Vinti, G., Approximation by nonlinear singular integral oper- ators in some modular function spaces. Ann. Polon. Math. 63 (2) (1996), 173-182.
  • Bardaro, C., Musielak, J. and Vinti, G., Nonlinear Integral Operators and Applications. De Gruyter Ser. Nonlinear Anal. Appl. 9, Walter de Gruyter, Berlin (2003).
  • Bardaro, C., Karsli, H. and Vinti, G., On pointwise convergence of Mellin type nonlinear m-singular integral operators. Comm. Appl. Nonlinear Anal. 20 (2) (2013), 25–39.
  • Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation vol. I. Academic Press, New York, London (1971).
  • Carlsson, M., Fatou-type theorems for general approximate identities. Math. Scand. 102 (2) (2008), 231–252.
  • Donoghue, W. F. J., A theorem of the Fatou type. Monatsh. Math. 67 (1963), 225–228.
  • Fatou, P., Séries trigonométriques et séries de Taylor. Acta Math. 30(1) (1906), 335–400.
  • Gadjiev, A. D., The order of convergence of singular integrals which depend on two parame- ters. In: Special Problems of Functional Analysis and their Appl. to the Theory of Diğ. Eq. and the Theory of Func., Izdat. Akad. Nauk Azerba¼ıdaµzan. SSR., (1968), 40–44.
  • Gadjiev, A. D., On nearness to zero of a family of nonlinear integral operators of Hammerstein. Izv. Akad. Nauk Azerba¼ıdµzan. SSR Ser. Fiz.-Tehn. Mat. Nauk, 2 (1966), 32-34.
  • Gripenberg, G., Londen, S. O. and Stağans, O., Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications, no. 34, Cambridge University Press, Cam- bridge (1990).
  • Ibrahimov, E. J. and Jafarova, S. A., On convergence and convergence order of Gegenbauer’s m-singular integrals. Proc. A. Razmadze Math. Inst. 159 (2012), 21–42.
  • Karsli, H. and Ibikli, E., On convergence of convolution type singular integral operators depending on two parameters. Fasc. Math. 38 (2007), 25–39.
  • Karsli, H., Fatou type convergence of nonlinear m-singular integral operators. Appl. Math. Comput. 246 (2014), 221–228.
  • Loomis, L. H., The converse of the Fatou theorem for positive harmonic functions. Trans. Amer. Math. Soc. 53 (1943), 239–250.
  • Mamedov, R. G., On the order of convergence of m-singular integrals at generalized Lebesgue points and in the space Lp( 1; 1). Izv. Akad. Nauk SSSR Ser. Mat. 27 (2) (1963), 287-304.
  • Musielak, J., On some approximation problems in modular spaces. In: Constructive Function Theory 1981, (Proc. Int. Conf., Varna, June 1-5, 1981). Publ. House Bulgarian Acad. Sci., So…a (1983), 455-461.
  • Musielak, J., Approximation by nonlinear singular integral operators in generalized Orlicz spaces. Comment. Math. Prace Mat. 31 (1991), 79–88.
  • Musielak, J., Nonlinear approximation in some modular function spaces: I. Math. Japonica, (1993), 83-90.
  • Rudin, W., Real and Complex Analysis. Mc-Graw Hill Book Co., London (1987).
  • Rydzewska, B., Approximation des fonctions par des intégrales singulières ordinaires. Fasc. Math. 7 (1973), 71–81.
  • Rydzewska, B., Point-approximation des fonctions par des certaines intégrales singulières. Fasc. Math. 10 (1978), 13–24.
  • Siudut, S., On the Fatou type convergence of abstract singular integrals. Comment. Math. Prace Mat. 30 (1) (1990), 171–176.
  • Stein, E. M., Singular Integrals and Diğerentiability Properties of Functions. Princeton Uni- versity Press, New Jersey (1970).
  • Swiderski, T. and Wachnicki, E., Nonlinear singular integrals depending on two parameters. Comment Math. 40 (2000), 181–189.
  • Taberski, R., Singular integrals depending on two parameters. Prace Mat. 7 (1962), 173-179.
  • Taberski, R., On double integrals and Fourier series. Ann. Polon. Math. 15 (1964), 97–115.
  • Taberski, R., On double singular integrals. Prace Mat. 19 (1976), 155–160.
  • Uysal, G. and Ibikli, E., Weighted approximation by double singular integral operators with radially de…ned kernels. Math. Sci. (Springer) 10 (4) (2016), 149–157.
  • Current address : Department of Computer Technologies, Division of Technology of Information Security, Karabuk University, Karabuk 78050, TURKEY
Yıl 2018, Cilt: 67 Sayı: 1, 262 - 276, 01.02.2018
https://doi.org/10.1501/Commua1_0000000848

Öz

Kaynakça

  • Alexits, G., Convergence problems of orthogonal series. Translated from the German by I. Földer, International Series of Monographs in Pure and Applied Mathematics vol. 20, Pergamon Press, New York (1961).
  • Bardaro, C., On approximation properties for some classes of linear operators of convolution type. Atti Sem. Mat. Fis. Univ. Modena, 33 (1984), 329-356.
  • Bardaro, C., Musielak, J. and Vinti, G., Approximation by nonlinear singular integral oper- ators in some modular function spaces. Ann. Polon. Math. 63 (2) (1996), 173-182.
  • Bardaro, C., Musielak, J. and Vinti, G., Nonlinear Integral Operators and Applications. De Gruyter Ser. Nonlinear Anal. Appl. 9, Walter de Gruyter, Berlin (2003).
  • Bardaro, C., Karsli, H. and Vinti, G., On pointwise convergence of Mellin type nonlinear m-singular integral operators. Comm. Appl. Nonlinear Anal. 20 (2) (2013), 25–39.
  • Butzer, P. L. and Nessel, R. J., Fourier Analysis and Approximation vol. I. Academic Press, New York, London (1971).
  • Carlsson, M., Fatou-type theorems for general approximate identities. Math. Scand. 102 (2) (2008), 231–252.
  • Donoghue, W. F. J., A theorem of the Fatou type. Monatsh. Math. 67 (1963), 225–228.
  • Fatou, P., Séries trigonométriques et séries de Taylor. Acta Math. 30(1) (1906), 335–400.
  • Gadjiev, A. D., The order of convergence of singular integrals which depend on two parame- ters. In: Special Problems of Functional Analysis and their Appl. to the Theory of Diğ. Eq. and the Theory of Func., Izdat. Akad. Nauk Azerba¼ıdaµzan. SSR., (1968), 40–44.
  • Gadjiev, A. D., On nearness to zero of a family of nonlinear integral operators of Hammerstein. Izv. Akad. Nauk Azerba¼ıdµzan. SSR Ser. Fiz.-Tehn. Mat. Nauk, 2 (1966), 32-34.
  • Gripenberg, G., Londen, S. O. and Stağans, O., Volterra Integral and Functional Equations, Encyclopedia of Mathematics and its Applications, no. 34, Cambridge University Press, Cam- bridge (1990).
  • Ibrahimov, E. J. and Jafarova, S. A., On convergence and convergence order of Gegenbauer’s m-singular integrals. Proc. A. Razmadze Math. Inst. 159 (2012), 21–42.
  • Karsli, H. and Ibikli, E., On convergence of convolution type singular integral operators depending on two parameters. Fasc. Math. 38 (2007), 25–39.
  • Karsli, H., Fatou type convergence of nonlinear m-singular integral operators. Appl. Math. Comput. 246 (2014), 221–228.
  • Loomis, L. H., The converse of the Fatou theorem for positive harmonic functions. Trans. Amer. Math. Soc. 53 (1943), 239–250.
  • Mamedov, R. G., On the order of convergence of m-singular integrals at generalized Lebesgue points and in the space Lp( 1; 1). Izv. Akad. Nauk SSSR Ser. Mat. 27 (2) (1963), 287-304.
  • Musielak, J., On some approximation problems in modular spaces. In: Constructive Function Theory 1981, (Proc. Int. Conf., Varna, June 1-5, 1981). Publ. House Bulgarian Acad. Sci., So…a (1983), 455-461.
  • Musielak, J., Approximation by nonlinear singular integral operators in generalized Orlicz spaces. Comment. Math. Prace Mat. 31 (1991), 79–88.
  • Musielak, J., Nonlinear approximation in some modular function spaces: I. Math. Japonica, (1993), 83-90.
  • Rudin, W., Real and Complex Analysis. Mc-Graw Hill Book Co., London (1987).
  • Rydzewska, B., Approximation des fonctions par des intégrales singulières ordinaires. Fasc. Math. 7 (1973), 71–81.
  • Rydzewska, B., Point-approximation des fonctions par des certaines intégrales singulières. Fasc. Math. 10 (1978), 13–24.
  • Siudut, S., On the Fatou type convergence of abstract singular integrals. Comment. Math. Prace Mat. 30 (1) (1990), 171–176.
  • Stein, E. M., Singular Integrals and Diğerentiability Properties of Functions. Princeton Uni- versity Press, New Jersey (1970).
  • Swiderski, T. and Wachnicki, E., Nonlinear singular integrals depending on two parameters. Comment Math. 40 (2000), 181–189.
  • Taberski, R., Singular integrals depending on two parameters. Prace Mat. 7 (1962), 173-179.
  • Taberski, R., On double integrals and Fourier series. Ann. Polon. Math. 15 (1964), 97–115.
  • Taberski, R., On double singular integrals. Prace Mat. 19 (1976), 155–160.
  • Uysal, G. and Ibikli, E., Weighted approximation by double singular integral operators with radially de…ned kernels. Math. Sci. (Springer) 10 (4) (2016), 149–157.
  • Current address : Department of Computer Technologies, Division of Technology of Information Security, Karabuk University, Karabuk 78050, TURKEY
Toplam 31 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Research Article
Yazarlar

Gümrah Uysal Bu kişi benim

Yayımlanma Tarihi 1 Şubat 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 67 Sayı: 1

Kaynak Göster

APA Uysal, G. (2018). NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 67(1), 262-276. https://doi.org/10.1501/Commua1_0000000848
AMA Uysal G. NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2018;67(1):262-276. doi:10.1501/Commua1_0000000848
Chicago Uysal, Gümrah. “NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67, sy. 1 (Şubat 2018): 262-76. https://doi.org/10.1501/Commua1_0000000848.
EndNote Uysal G (01 Şubat 2018) NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67 1 262–276.
IEEE G. Uysal, “NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 67, sy. 1, ss. 262–276, 2018, doi: 10.1501/Commua1_0000000848.
ISNAD Uysal, Gümrah. “NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 67/1 (Şubat 2018), 262-276. https://doi.org/10.1501/Commua1_0000000848.
JAMA Uysal G. NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67:262–276.
MLA Uysal, Gümrah. “NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 67, sy. 1, 2018, ss. 262-76, doi:10.1501/Commua1_0000000848.
Vancouver Uysal G. NONLINEARm SINGULAR INTEGRAL OPERATORS IN THE FRAMEWORK OF FATOU TYPE WEIGHTED CONVERGENCE. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2018;67(1):262-76.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.