Öz
Bu çalışma reel eksen üzerinde tanımlı sürekli fonksiyonların ağırlıklı uzayında tanımlı doğrusal pozitif operatörlerin q benzerleri ile ilgilidir. q analizi kullanarak, sınırsız kümeler üzerinde tanımlı, sınırsız ve sürekli fonksiyonların uzayında Korovkin teoreminin varlığını araştıracağız
Anahtar Kelimeler
Korovkin teoremi Doğrusal pozitif operatörler Q-analiz Ağırlıklı uzay
Kaynakça
- Coskun, T., 1997. Some Properties of Linear Positive Operators in the Weighted Spaces of Unbounded Functions., Commun. Fac. Sci. Univ. Ank. Series, 47: 175-191.
- Coskun, T., 2012. On the Order of Weighted Approximation of by Sequences of Positive Linear Operators., Turk J Math., 36: 113-120.
- Ernst, T., A., 2012. Comprehensive Treatment of q-Calculus, Birkhauser, pp.1-200.
- Gadjiev, A. D., 1976. On P. P. Korovkin Type Theorems., Math. Zametki, 20(5):995-998.
- Gadjiev, A. D., 1974. The Convergence Problem for a Sequence of Positive Linear Operators on Unbounded Sets and Theorems Analogous To That of P. P. Korovkin , Engl. Translated. Sov. Math. Dokl., 15: 1433-1436.
- Gadjiev and Hacisalihoglu, 1995. On convergence of the sequences of linear positive operators, Ankara University, in Turkish.
- Korovkin, P. P. 1960. Linear Operators and Approximation Theory, Hindustan Publishing Corp., 219: 1-20.
- Lupas, A., 1987. A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus, University of Cluj- Napoca, 9, 85-92.
- Phillips, G.M., 1997. Bernstein polynomials based on the q-integers, The heritage of P.L.Chebyshev, Ann. Numer.Math., 4, 511-518.
- Videnskii, V S., 2005. On some classes of q-parametric positive operators, Operator Theory Adv. Appl., 158, 213-222.
Öz
This paper deals with q-analogues of linear positive operators defined in weighted space of continuous functions defined on real axis. We study, using q-calculus, the existence of Korovkin's theorem in the spaces of continuous and unbounded functions defined on unbounded sets.
Anahtar Kelimeler
Linear Positive Operator Korovkin Theorem q-calculus Weighted space.
Kaynakça
- Coskun, T., 1997. Some Properties of Linear Positive Operators in the Weighted Spaces of Unbounded Functions., Commun. Fac. Sci. Univ. Ank. Series, 47: 175-191.
- Coskun, T., 2012. On the Order of Weighted Approximation of by Sequences of Positive Linear Operators., Turk J Math., 36: 113-120.
- Ernst, T., A., 2012. Comprehensive Treatment of q-Calculus, Birkhauser, pp.1-200.
- Gadjiev, A. D., 1976. On P. P. Korovkin Type Theorems., Math. Zametki, 20(5):995-998.
- Gadjiev, A. D., 1974. The Convergence Problem for a Sequence of Positive Linear Operators on Unbounded Sets and Theorems Analogous To That of P. P. Korovkin , Engl. Translated. Sov. Math. Dokl., 15: 1433-1436.
- Gadjiev and Hacisalihoglu, 1995. On convergence of the sequences of linear positive operators, Ankara University, in Turkish.
- Korovkin, P. P. 1960. Linear Operators and Approximation Theory, Hindustan Publishing Corp., 219: 1-20.
- Lupas, A., 1987. A q-analogue of the Bernstein operator, Seminar on Numerical and Statistical Calculus, University of Cluj- Napoca, 9, 85-92.
- Phillips, G.M., 1997. Bernstein polynomials based on the q-integers, The heritage of P.L.Chebyshev, Ann. Numer.Math., 4, 511-518.
- Videnskii, V S., 2005. On some classes of q-parametric positive operators, Operator Theory Adv. Appl., 158, 213-222.
Ayrıntılar
| Birincil Dil | Türkçe |
|---|---|
| Bölüm | Research Article |
| Yazarlar | |
| Yayımlanma Tarihi | 1 Ocak 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 7 Sayı: 1 |