Araştırma Makalesi
Yıl 2024,
Cilt: 16 Sayı: 2, 358 - 366, 31.12.2024
Öz
In this paper, we focus on two summability methods and investigate some applications of them for the Cheney-Sharma operators. We obtain approximation properties of the Cheney-Sharma operators via power series statistical convergence. We also analyze the convergence rates employing both the modulus of continuity and elements of the Lipschitz class. Additionally, we define r-th order generalization of the these operators which is linear but don't satisfy the positivity property and investigate approximation properties of these operators, via A-statistical convergence. We support our results with an example and a graph.
Anahtar Kelimeler
Cheney-Sharma operators power series statistical convergence rate of convergence rth order generalizations A-statistical convergence
Kaynakça
- Agratini, O., Statistical convergence of non-positive approximation process, Chaos Solitions Fractals, 44(11)(2011), 977–981.
- Altomare, F., Campiti, M., Korovkin-type Approximaton Theory and Its Applications, Walter de Gruyter, Berlin-New York, 1994.
- Başcanbaz-Tunca, G., Erençin, A., Taşdelen, F., Some properties of Bernstein type Cheney and Sharma operators, Gen. Math., 24(1-2)(2016), 17–25.
- Boos, J., Classical and Modern Methods in Summability, Oxford University Press, Oxford, 2000.
- Bostancı, T., Başcanbaz-Tunca, G., Stancu type extension of Cheney and Sharma operators, J. Numer. Anal. Approx. Theory, 47(2)(2018), 124–134.
- Cheney, E.W., Sharma, A., On a generalization of Bernstein polynomials, Riv. Mat. Univ.Parma, 2(5)(1964), 77–84.
- Duman O., Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(1-2)(2006), 33–46.
- Duman, O., A Korovkin type approximation theorems via I-convergence, Czechoslovak Math. J., 57(132)(2007), 367–375.
- Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
- Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32(2002), 129–138.
- Kirov, G.H., Popova, L. A generalization of the linear positive operators, Math. Balkanica, 7(1993), 149–162.
- Olgun, A., İnce, H.G., Taşdelen, F., Kantorovich-type generalization of Meyer -Könıg and Zeller operators via generating functions, An. S¸ t. Univ. Ovidius Constanta, 21(3)(2013), 209–221.
- Örkçü, M., Approximation properties of Stancu-type Meyer -Ko¨nig and Zeller Operators, Hacet. J. Math. Stat., 42(2)(2013), 139–148.
- Özarslan, M.A., Duman, O., Doğru, O., Rates of A-statistical convergence of approximating operators, Calcolo, 42(2005), 93–104.
- Özarslan, M.A., Duman, O. Srivastava, H.M., Statistical approximation results for Kantorovich-type operators involving some special polynomials, Math. Comput Modelling, 48(2008), 388–401.
- Prakash, C., Verma, D.K., Deo, N., Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators, Mathematical Foundations of Computing, 6(3)(2023), 535–545.
- Sakaoglu, İ., Ünver, M., Statistical approximation for multivariable integrable functions, Miskolc Math. Notes, 13(2012), 485–491.
- Salat, T., On statistically convergent sequences of real numbers, Mat.Slovaca., 30(2)(1980), 139–150.
- Söylemez, D., Ünver, M. Korovkin type theorems for Cheney–Sharma Operators via summability methods, Results Math., 73(2017), 1601–1612.
- Söylemez, D., Taşdelen. F., On Cheney-Sharma Chlodovsky operators, Bulletin of Mathematical Analysis & Applications, 11(1)(2019).
- Söylemez D., Taşdelen, F., Approximation by Cheney-Sharma Chlodovsky operators, Hacettepe J. Math. Stat., 49(2020), 510–522.
- Söylemez, D., Ünver, M., Rates of power series statistical convergence of positive linear operators and power series statistical convergence of-Meyer–König and Zeller Operators, Lobachevskii J. Math., 42(2)(2021), 426–434.
- Srivastava, H.M., Ansari, K.J., Özger, F., Ödemis¸ Özger, Z., A link between approximation theory and summability methods via fourdimensional infinite matrices, Mathematics, 9(16)(2021), 1895.
- Stancu, D.D., Cismaşiu, C., On an approximating linear positive operator of Cheney-Sharma, Rev. Anal. Num´er. Th´eor. Approx., 26(1-2)(1997), 221–227.
- Stancu, D.D., Stoica, E.I., On the use Abel-Jensen type combinatorial formulas for construction and investigation of some algebraic polynomial operators of approximation, Stud. Univ. Babes¸ Bolyai Math., 54(4)(2009), 167–182.
- Taş, E., Yurdakadim, T., Approximation to derivatives of functions by linear operators acting on weighted spaces by power series method, Computational analysis, Springer Proceedings in Mathematics and Statistics, 155(2016), 363–372.
- Taş, E., Yurdakadim, T., Atlıhan, Ö .G., Korovkin type approximation theorems in weighted spaces via power series method, Oper. Matrices, 12(2)(2018), 529–535.
- Uluçay, H., Ünver,M., Söylemez, D., Some Korovkin type approximation applications of power series methods, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117(1)(2023), 1–24.
- Ünver, M., Khan, M.K., Orhan, C, A-distributional summability in topological spaces, Positivity, 18(1)(2014), 131–145.
- Ünver, M., Orhan, C., Statistical convergence with respect to power series methods and applications to approximation theory, Journal Numerical Functional Analysis and Optimization, 40(5)(2019), 535–547.
Yıl 2024,
Cilt: 16 Sayı: 2, 358 - 366, 31.12.2024
Öz
Kaynakça
- Agratini, O., Statistical convergence of non-positive approximation process, Chaos Solitions Fractals, 44(11)(2011), 977–981.
- Altomare, F., Campiti, M., Korovkin-type Approximaton Theory and Its Applications, Walter de Gruyter, Berlin-New York, 1994.
- Başcanbaz-Tunca, G., Erençin, A., Taşdelen, F., Some properties of Bernstein type Cheney and Sharma operators, Gen. Math., 24(1-2)(2016), 17–25.
- Boos, J., Classical and Modern Methods in Summability, Oxford University Press, Oxford, 2000.
- Bostancı, T., Başcanbaz-Tunca, G., Stancu type extension of Cheney and Sharma operators, J. Numer. Anal. Approx. Theory, 47(2)(2018), 124–134.
- Cheney, E.W., Sharma, A., On a generalization of Bernstein polynomials, Riv. Mat. Univ.Parma, 2(5)(1964), 77–84.
- Duman O., Orhan, C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 69(1-2)(2006), 33–46.
- Duman, O., A Korovkin type approximation theorems via I-convergence, Czechoslovak Math. J., 57(132)(2007), 367–375.
- Fast, H., Sur la convergence statistique, Colloq. Math., 2(1951), 241–244.
- Gadjiev, A.D., Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32(2002), 129–138.
- Kirov, G.H., Popova, L. A generalization of the linear positive operators, Math. Balkanica, 7(1993), 149–162.
- Olgun, A., İnce, H.G., Taşdelen, F., Kantorovich-type generalization of Meyer -Könıg and Zeller operators via generating functions, An. S¸ t. Univ. Ovidius Constanta, 21(3)(2013), 209–221.
- Örkçü, M., Approximation properties of Stancu-type Meyer -Ko¨nig and Zeller Operators, Hacet. J. Math. Stat., 42(2)(2013), 139–148.
- Özarslan, M.A., Duman, O., Doğru, O., Rates of A-statistical convergence of approximating operators, Calcolo, 42(2005), 93–104.
- Özarslan, M.A., Duman, O. Srivastava, H.M., Statistical approximation results for Kantorovich-type operators involving some special polynomials, Math. Comput Modelling, 48(2008), 388–401.
- Prakash, C., Verma, D.K., Deo, N., Approximation by Durrmeyer variant of Cheney-Sharma Chlodovsky operators, Mathematical Foundations of Computing, 6(3)(2023), 535–545.
- Sakaoglu, İ., Ünver, M., Statistical approximation for multivariable integrable functions, Miskolc Math. Notes, 13(2012), 485–491.
- Salat, T., On statistically convergent sequences of real numbers, Mat.Slovaca., 30(2)(1980), 139–150.
- Söylemez, D., Ünver, M. Korovkin type theorems for Cheney–Sharma Operators via summability methods, Results Math., 73(2017), 1601–1612.
- Söylemez, D., Taşdelen. F., On Cheney-Sharma Chlodovsky operators, Bulletin of Mathematical Analysis & Applications, 11(1)(2019).
- Söylemez D., Taşdelen, F., Approximation by Cheney-Sharma Chlodovsky operators, Hacettepe J. Math. Stat., 49(2020), 510–522.
- Söylemez, D., Ünver, M., Rates of power series statistical convergence of positive linear operators and power series statistical convergence of-Meyer–König and Zeller Operators, Lobachevskii J. Math., 42(2)(2021), 426–434.
- Srivastava, H.M., Ansari, K.J., Özger, F., Ödemis¸ Özger, Z., A link between approximation theory and summability methods via fourdimensional infinite matrices, Mathematics, 9(16)(2021), 1895.
- Stancu, D.D., Cismaşiu, C., On an approximating linear positive operator of Cheney-Sharma, Rev. Anal. Num´er. Th´eor. Approx., 26(1-2)(1997), 221–227.
- Stancu, D.D., Stoica, E.I., On the use Abel-Jensen type combinatorial formulas for construction and investigation of some algebraic polynomial operators of approximation, Stud. Univ. Babes¸ Bolyai Math., 54(4)(2009), 167–182.
- Taş, E., Yurdakadim, T., Approximation to derivatives of functions by linear operators acting on weighted spaces by power series method, Computational analysis, Springer Proceedings in Mathematics and Statistics, 155(2016), 363–372.
- Taş, E., Yurdakadim, T., Atlıhan, Ö .G., Korovkin type approximation theorems in weighted spaces via power series method, Oper. Matrices, 12(2)(2018), 529–535.
- Uluçay, H., Ünver,M., Söylemez, D., Some Korovkin type approximation applications of power series methods, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 117(1)(2023), 1–24.
- Ünver, M., Khan, M.K., Orhan, C, A-distributional summability in topological spaces, Positivity, 18(1)(2014), 131–145.
- Ünver, M., Orhan, C., Statistical convergence with respect to power series methods and applications to approximation theory, Journal Numerical Functional Analysis and Optimization, 40(5)(2019), 535–547.
Toplam 30 adet kaynakça vardır.
Ayrıntılar
| Birincil Dil | İngilizce |
|---|---|
| Konular | Yaklaşım Teorisi ve Asimptotik Yöntemler |
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 31 Aralık 2024 |
| Gönderilme Tarihi | 26 Aralık 2023 |
| Kabul Tarihi | 17 Temmuz 2024 |
| Yayımlandığı Sayı | Yıl 2024 Cilt: 16 Sayı: 2 |