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Yıl 2023, Cilt: 6 Sayı: 4, 237 - 248, 15.12.2023

Ali Aral

https://doi.org/10.33205/cma.1381787

Öz

Kaynakça

  • A. M. Acu, G. Bascanbaz Tunca and I. Ra¸sa: Information potential for some probability density functions, Appl. Math. Comput., 389 (2021), 1–15.
  • L. Angeloni, G. Vinti: Convergence and rate of approximation in BV ϕ (RN) for a class of Mellin integral operators, Rend. Lincei-Mat. Appl., 25 (3) (2014), 217–232.
  • L. Angeloni, G. Vinti: Approximation in variation for Mellin integral operators, PAMM, 15 (1) (2015), 649–650.
  • L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini and G. Vinti: Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces, Constr. Math. Anal., 4 (2) (2021), 229–241.
  • A. Aral, T. Acar and S. Kursun: Generalized Kantorovich forms of exponential sampling series, Anal. Math. Phys., 12 (2) (2022), 1–19.
  • A. Aral, F. Ozsarac and B. Yilmaz: Quantitative type theorems in the space of locally integrable functions, Positivity, 26 (3) (2022), 1–13.
  • C. Bardaro, I. Mantellini: A note on the Voronovskaja theorem for Mellin–Fejer convolution operators, Appl. Math. Lett., 24 (12) (2011), 2064–2067.
  • C. Bardaro, I. Mantellini: Approximation properties for linear combinations of moment type operators, Comput. Math. Appl., 62 (5) (2011), 2304–2313.
  • C. Bardaro, I. Mantellini: Asymptotic behaviour of Mellin–Fejer convolution operators, East J. Approx., 17 (2) (2011), 181–201.
  • C. Bardaro, I. Mantellini: Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces, Mathematical Foundations of Computing, 5 (3) (2022), 219–229.
  • C. Bardaro, I. Mantellini: On Mellin convolution operators: a direct approach to the asymptotic formulae, Integral Transf. Spec. Funct., 25 (3) (2014), 182–195.
  • C. Bardaro, I. Mantellini: On the iterates of Mellin–Fejer convolution operators, Acta Appl. Math., 121 (1) (2012), 213–229.
  • C. Bardaro, I. Mantellini: Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math., 27 (4) (2006), 431–447.
  • C. Bardaro, I. Mantellini: Voronovskaya-type estimates for Mellin convolution operators, Res. Math., 1 (50) (2007), 1–16.
  • C. Bardaro, G. Bevignani, I. Mantellını, M. Seracini, Bivariate Generalized Exponential Sampling Series and Applications to Seismic Waves, Constr. Math. Anal., 2 (4) (2019), 153–167.
  • C. Bardaro, I. Mantellini and I. Tittarelli: Convergence of semi-discrete exponential sampling operators in Mellin-Lebesgue spaces, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117 (30), (2023) 1–15.
  • S. J. Bernau: Theorems of Korovkin type for Lp spaces, Pacific J. Math., 53 (1) (1974), 11–19.
  • M. Bertero, E. Pike: Exponential-sampling method for Laplace and other dilationally invariant transforms: I. Singular system analysis, Inverse Probl., 7 (1) (1991), 1–20.
  • M. Bertero, E. Pike: Exponential-sampling method for Laplace and other dilationally invariant transforms: II. Examples in photon correlation spectroscopy and fraunhofer diffraction, Inverse Probl., 7 (1) (1991), 21–41.
  • P. L. Butzer, S. Jansche: A direct approach to the Mellin transform, J. Fourier Anal. Appl., 3 (1997), 325–375.
  • P. L. Butzer, S. Jansche: The exponential sampling theorem of signal analysis, Atti Semin. Mat. Fis. Univ. Modena, 46 (1998), 99–122.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Vol 1, Birkhauser, Basel and Academic Press, New York (1971).
  • D. Costarelli, G. Vinti: A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces, Constr. Math. Anal., 2 (1) (2019), 8–14.
  • K. Donne: Korovkin Theorems in Lp-spaces, J. Funct. Anal., 42 (1) (1981), 12–28.
  • O. Duman, C. Orhan: Rates of A- statistical convergence of operators in the space of locally integrable functions, Appl. Math. Lett., 21 (5) (2008), 431–435.
  • A. D. Gadjiev, A. Aral: Weighted Lp-approximation with positive linear operators on unbounded sets, Appl. Math. Lett., 20 (10) (2007), 1046–1051.
  • A. D. Gadjiev, R. O. Efendiyev and E. ˙Ibikli: On Korovkin’s type theorem in the space of locally integrable functions, Czechoslovak Math. J., 53 (128) (2003),: 45–53.
  • W. Kitto, D. E. Walbert: Korovkin approximations in Lp-spaces, Pacific J. Math., 63 (1) (1976), 153–167.
  • W. Kolbe, R. J. Nessel: Saturation theory in connection with Mellin transform methods, SIAM J. Math Anal., 3 (2) (1972), 246–262.
  • R. Mamedov: The Mellin Transform and Approximation Theory, Elm, Baku (1991).
  • T. Nishishiraho: Quantitative theorems on linear approximation processes of convolution operators in Banach spaces, Tohoku Math. J., 33 (1) (1981), 109–126.
  • F. Ozsarac, A. M. Acu, A. Aral and I. Ra¸sa: On the Modification of Mellin Convolution Operator and Its Associated Information Potential, Numer. Funct. Anal. Optim., 44 (11) (2023), 1194–1208.

On a new approach in the space of measurable functions

Yıl 2023, Cilt: 6 Sayı: 4, 237 - 248, 15.12.2023

Ali Aral

https://doi.org/10.33205/cma.1381787

Öz

In this paper, we present a new modulus of continuity for locally integrable function spaces which is effected by the natural structure of the L_{p} space. After basic properties of it are expressed, we provide a quantitative type theorem for the rate of convergence of convolution type integral operators and iterates of them. Moreover, we state their global smoothness preservation property including the new modulus of continuity. Finally, the obtained results are performed to the Gauss-Weierstrass operators.

Anahtar Kelimeler

Convolution type integral operators measurable functions weighted modulus of continuity.

Kaynakça

  • A. M. Acu, G. Bascanbaz Tunca and I. Ra¸sa: Information potential for some probability density functions, Appl. Math. Comput., 389 (2021), 1–15.
  • L. Angeloni, G. Vinti: Convergence and rate of approximation in BV ϕ (RN) for a class of Mellin integral operators, Rend. Lincei-Mat. Appl., 25 (3) (2014), 217–232.
  • L. Angeloni, G. Vinti: Approximation in variation for Mellin integral operators, PAMM, 15 (1) (2015), 649–650.
  • L. Angeloni, N. Çetin, D. Costarelli, A. R. Sambucini and G. Vinti: Multivariate sampling Kantorovich operators: quantitative estimates in Orlicz spaces, Constr. Math. Anal., 4 (2) (2021), 229–241.
  • A. Aral, T. Acar and S. Kursun: Generalized Kantorovich forms of exponential sampling series, Anal. Math. Phys., 12 (2) (2022), 1–19.
  • A. Aral, F. Ozsarac and B. Yilmaz: Quantitative type theorems in the space of locally integrable functions, Positivity, 26 (3) (2022), 1–13.
  • C. Bardaro, I. Mantellini: A note on the Voronovskaja theorem for Mellin–Fejer convolution operators, Appl. Math. Lett., 24 (12) (2011), 2064–2067.
  • C. Bardaro, I. Mantellini: Approximation properties for linear combinations of moment type operators, Comput. Math. Appl., 62 (5) (2011), 2304–2313.
  • C. Bardaro, I. Mantellini: Asymptotic behaviour of Mellin–Fejer convolution operators, East J. Approx., 17 (2) (2011), 181–201.
  • C. Bardaro, I. Mantellini: Boundedness properties of semi-discrete sampling operators in Mellin–Lebesgue spaces, Mathematical Foundations of Computing, 5 (3) (2022), 219–229.
  • C. Bardaro, I. Mantellini: On Mellin convolution operators: a direct approach to the asymptotic formulae, Integral Transf. Spec. Funct., 25 (3) (2014), 182–195.
  • C. Bardaro, I. Mantellini: On the iterates of Mellin–Fejer convolution operators, Acta Appl. Math., 121 (1) (2012), 213–229.
  • C. Bardaro, I. Mantellini: Pointwise convergence theorems for nonlinear Mellin convolution operators, Int. J. Pure Appl. Math., 27 (4) (2006), 431–447.
  • C. Bardaro, I. Mantellini: Voronovskaya-type estimates for Mellin convolution operators, Res. Math., 1 (50) (2007), 1–16.
  • C. Bardaro, G. Bevignani, I. Mantellını, M. Seracini, Bivariate Generalized Exponential Sampling Series and Applications to Seismic Waves, Constr. Math. Anal., 2 (4) (2019), 153–167.
  • C. Bardaro, I. Mantellini and I. Tittarelli: Convergence of semi-discrete exponential sampling operators in Mellin-Lebesgue spaces, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117 (30), (2023) 1–15.
  • S. J. Bernau: Theorems of Korovkin type for Lp spaces, Pacific J. Math., 53 (1) (1974), 11–19.
  • M. Bertero, E. Pike: Exponential-sampling method for Laplace and other dilationally invariant transforms: I. Singular system analysis, Inverse Probl., 7 (1) (1991), 1–20.
  • M. Bertero, E. Pike: Exponential-sampling method for Laplace and other dilationally invariant transforms: II. Examples in photon correlation spectroscopy and fraunhofer diffraction, Inverse Probl., 7 (1) (1991), 21–41.
  • P. L. Butzer, S. Jansche: A direct approach to the Mellin transform, J. Fourier Anal. Appl., 3 (1997), 325–375.
  • P. L. Butzer, S. Jansche: The exponential sampling theorem of signal analysis, Atti Semin. Mat. Fis. Univ. Modena, 46 (1998), 99–122.
  • P. L. Butzer, R. J. Nessel: Fourier Analysis and Approximation, Vol 1, Birkhauser, Basel and Academic Press, New York (1971).
  • D. Costarelli, G. Vinti: A Quantitative Estimate for the Sampling Kantorovich Series in Terms of the Modulus of Continuity in Orlicz Spaces, Constr. Math. Anal., 2 (1) (2019), 8–14.
  • K. Donne: Korovkin Theorems in Lp-spaces, J. Funct. Anal., 42 (1) (1981), 12–28.
  • O. Duman, C. Orhan: Rates of A- statistical convergence of operators in the space of locally integrable functions, Appl. Math. Lett., 21 (5) (2008), 431–435.
  • A. D. Gadjiev, A. Aral: Weighted Lp-approximation with positive linear operators on unbounded sets, Appl. Math. Lett., 20 (10) (2007), 1046–1051.
  • A. D. Gadjiev, R. O. Efendiyev and E. ˙Ibikli: On Korovkin’s type theorem in the space of locally integrable functions, Czechoslovak Math. J., 53 (128) (2003),: 45–53.
  • W. Kitto, D. E. Walbert: Korovkin approximations in Lp-spaces, Pacific J. Math., 63 (1) (1976), 153–167.
  • W. Kolbe, R. J. Nessel: Saturation theory in connection with Mellin transform methods, SIAM J. Math Anal., 3 (2) (1972), 246–262.
  • R. Mamedov: The Mellin Transform and Approximation Theory, Elm, Baku (1991).
  • T. Nishishiraho: Quantitative theorems on linear approximation processes of convolution operators in Banach spaces, Tohoku Math. J., 33 (1) (1981), 109–126.
  • F. Ozsarac, A. M. Acu, A. Aral and I. Ra¸sa: On the Modification of Mellin Convolution Operator and Its Associated Information Potential, Numer. Funct. Anal. Optim., 44 (11) (2023), 1194–1208.
Toplam 32 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Yaklaşım Teorisi ve Asimptotik Yöntemler
Bölüm Makaleler
Yazarlar

Ali Aral 0000-0002-2024-8607

Erken Görünüm Tarihi 17 Kasım 2023
Yayımlanma Tarihi 15 Aralık 2023
Gönderilme Tarihi 26 Ekim 2023
Kabul Tarihi 15 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 4

Kaynak Göster

APA Aral, A. (2023). On a new approach in the space of measurable functions. Constructive Mathematical Analysis, 6(4), 237-248. https://doi.org/10.33205/cma.1381787
AMA Aral A. On a new approach in the space of measurable functions. CMA. Aralık 2023;6(4):237-248. doi:10.33205/cma.1381787
Chicago Aral, Ali. “On a New Approach in the Space of Measurable Functions”. Constructive Mathematical Analysis 6, sy. 4 (Aralık 2023): 237-48. https://doi.org/10.33205/cma.1381787.
EndNote Aral A (01 Aralık 2023) On a new approach in the space of measurable functions. Constructive Mathematical Analysis 6 4 237–248.
IEEE A. Aral, “On a new approach in the space of measurable functions”, CMA, c. 6, sy. 4, ss. 237–248, 2023, doi: 10.33205/cma.1381787.
ISNAD Aral, Ali. “On a New Approach in the Space of Measurable Functions”. Constructive Mathematical Analysis 6/4 (Aralık 2023), 237-248. https://doi.org/10.33205/cma.1381787.
JAMA Aral A. On a new approach in the space of measurable functions. CMA. 2023;6:237–248.
MLA Aral, Ali. “On a New Approach in the Space of Measurable Functions”. Constructive Mathematical Analysis, c. 6, sy. 4, 2023, ss. 237-48, doi:10.33205/cma.1381787.
Vancouver Aral A. On a new approach in the space of measurable functions. CMA. 2023;6(4):237-48.
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