Yıl 2018,
, 113 - 127, 07.11.2018
Ana Maria Acu
,
Sever Hodış
Ioan Raşa
Kaynakça
- [1] U. Abel, M. Ivan, Asymptotic expansion of the multivariate Bernstein polynomials on a simplex, Approx. Theory Appl.
16 (2000), 85-93.
- [2] A. M. Acu, I. Raşa, New estimates for the differences of positive linear operators, Numerical Algorithms 73(3) (2016),
775-789.
- [3] A. M. Acu, I. Raşa, Estimates for the differences of positive linear operators and their derivatives, arXiv:1810.08839v1,
submitted.
- [4] A. Aral, D. Inoan and I. Raşa, On differences of linear positive operators, Anal. Math. Phys.(2018). DOI
https://doi.org/10.1007/s1332
- [5] S. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Communications de la
Société Mathematique de Kharkov, 13 (1913), 1-2.
- [6] W. Chen, On the modified Bernstein-Durrmeyer operator, Report of the Fifth Chinese Conference on Approximation
Theory, Zhen Zhou, China, 1987.
- [7] H. Gonska, I. Ra¸sa, E.-D. Stanila, Beta operators with Jacobi weights, In: Constructive theory of functions, Sozopol
2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), 99–112. Prof. Marin Drinov Academic Publishing House, Sofia,
2014.
- [8] H. Gonska, I. Raşa, Differences of positive linear operators and the second order modulus, Carpathian J. Math. 24(3)
(2008), 332-340.
- [9] H. Gonska, P. Pitul, I. Ra¸sa, On differences of positive linear operators, Carpathian J. Math. 22(1-2) (2006), 65-78.
- [10] H. Gonska, P. Pitul, I. Ra¸sa, On Peano’s form of the Taylor remainder, Voronovskaja’s theorem and the commutator of
positive linear operators, in Numerical Analysis and Approximation Theory (Proc. Int. Conf. Cluj-Napoca 2006; ed.
by O. Agratini and P. Blaga), Cluj-Napoca, Casa C˘ar¸tii de ¸Stiin¸ta, 2006, 55-80.
- [11] H. Gonska, R. Paltanea, Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions,
Czechoslovak Math. J. 60(135) (2010), 783-799.
- [12] H. Gonska, R. Paltanea, Quantitative convergence theorems for a class of Bernstein-Durrmeyer operators preserving linear
functions, Ukrainian Math. J. 62 (2010), 913-922.
- [13] T. N. T. Goodman, A. Sharma, A modified Bernstein-Schoenberg operator, Proc. of the Conference on Constructive
Theory of Functions, Varna 1987 (ed. by Bl. Sendov et al.). Sofia: Publ. House Bulg. Acad. of Sci., 1988, 166-173.
- [14] M. Heilmann, F. Nasaireh, I. Ra¸sa, Complements to Voronovskaja’s formula, Chapter 11 In: D. Ghosh et al. (eds.),
Mathematics and Computing, Springer Proceedings in Mathematics & Statistics 253, Springer Nature Singapore
Pte Ltd. 2018, https://doi.org/10.1007/978-981-13-2095-8 11.
- [15] M. Heilmann, F. Nasaireh, I. Ra¸sa, Discrete Operators associated with Linking Operators, arXiv:1808.07239v1.
- [16] N. Ispir, On modified Baskakov operators on weighted spaces Turk. J. Math. 26(3) (2001), 355-365.
- [17] L.V. Kantorovich, Sur certain développements suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. URSS
563-568 (1930), 595-600.
- [18] A. Lupaş, The approximation by means of some linear positive operators, in Approximation Theory (M.W. Müller et al.,
eds), Akademie-Verlag, Berlin, 1995, 201-227.
- [19] A. Lupaş, Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart, 1972.
- [20] L. Lupaş, A. Lupa¸s, Polynomials of Binomial Type and Approximation Operators, Studia Univ. Babe¸s-Bolyai, Mathematica,
XXXII, 4 (1987), 61-70.
- [21] D.H. Mache, Gewichtete Simultanapproximation in der Lp-Metrik durch das Verfahren der Kantorovic Operatoren, Dissertation,
Univ. Dortmund, 1991.
- [22] D.H. Mache, A link between Bernstein polynomials and Durrmeyer polynomials with Jacobi weights, In: Approx. Theory
VIII, Vol. 1: Approximation and Interpolation, Ch.K. Chui and L.L. Schmaker (Eds.), 403-410, World Scientific
Publ., 1995.
- [23] S.M. Mazhar, V. Totik, Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257-269.
- [24] F. Nasaireh, I. Ra¸sa, Another look at Voronovskaya type formulas, Journal of Mathematical Inequalities, 12(1) (2018),
95-105.
- [25] F. Nasaireh, Voronovskaja-type formulas and applications, General Mathematics, 25(1-2) (2017), 37-43.
- [26] R. Paltanea, A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Sem. Funct. Equat.
Approxim. Convex. (Cluj-Napoca) 5 (2007), 109-117.
- [27] I. Raşa, Discrete operators associated with certain integral operators, Stud. Univ. Babe¸s- Bolyai Math., 56(2) (2011),
537-544.
- [28] I. Raşa, E. Stanila, On some operators linking the Bernstein and the genuine Bernstein-Durrmeyer operators, J. Appl.
Funct. Anal. 9 (2014), 369-378.
- [29] D. D. Stancu, Asupra unei generalizari a polinoamelor lui Bernstein, Stud. Univ. Babes-Bolyai Math. 14 (1969), 31-45.
- [30] E. D. Stanila, On Bernstein-Euler-Jacobi Operators, Ph D Thesis, Duisburg-Essen University, July, 2014.
- [31] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval J. Res. Natl. Bur. Stand. 45 (1950), 239-245.
A Survey on Estimates for the Differences of Positive Linear Operators
Yıl 2018,
, 113 - 127, 07.11.2018
Ana Maria Acu
,
Sever Hodış
Ioan Raşa
Öz
We survey some results concerning differences of positive linear operators from Approximation Theory, and present some new results in this direction.
Kaynakça
- [1] U. Abel, M. Ivan, Asymptotic expansion of the multivariate Bernstein polynomials on a simplex, Approx. Theory Appl.
16 (2000), 85-93.
- [2] A. M. Acu, I. Raşa, New estimates for the differences of positive linear operators, Numerical Algorithms 73(3) (2016),
775-789.
- [3] A. M. Acu, I. Raşa, Estimates for the differences of positive linear operators and their derivatives, arXiv:1810.08839v1,
submitted.
- [4] A. Aral, D. Inoan and I. Raşa, On differences of linear positive operators, Anal. Math. Phys.(2018). DOI
https://doi.org/10.1007/s1332
- [5] S. N. Bernstein, Démonstration du théorème de Weierstrass fondée sur le calcul des probabilités, Communications de la
Société Mathematique de Kharkov, 13 (1913), 1-2.
- [6] W. Chen, On the modified Bernstein-Durrmeyer operator, Report of the Fifth Chinese Conference on Approximation
Theory, Zhen Zhou, China, 1987.
- [7] H. Gonska, I. Ra¸sa, E.-D. Stanila, Beta operators with Jacobi weights, In: Constructive theory of functions, Sozopol
2013 (K. Ivanov, G. Nikolov and R. Uluchev, Eds.), 99–112. Prof. Marin Drinov Academic Publishing House, Sofia,
2014.
- [8] H. Gonska, I. Raşa, Differences of positive linear operators and the second order modulus, Carpathian J. Math. 24(3)
(2008), 332-340.
- [9] H. Gonska, P. Pitul, I. Ra¸sa, On differences of positive linear operators, Carpathian J. Math. 22(1-2) (2006), 65-78.
- [10] H. Gonska, P. Pitul, I. Ra¸sa, On Peano’s form of the Taylor remainder, Voronovskaja’s theorem and the commutator of
positive linear operators, in Numerical Analysis and Approximation Theory (Proc. Int. Conf. Cluj-Napoca 2006; ed.
by O. Agratini and P. Blaga), Cluj-Napoca, Casa C˘ar¸tii de ¸Stiin¸ta, 2006, 55-80.
- [11] H. Gonska, R. Paltanea, Simultaneous approximation by a class of Bernstein-Durrmeyer operators preserving linear functions,
Czechoslovak Math. J. 60(135) (2010), 783-799.
- [12] H. Gonska, R. Paltanea, Quantitative convergence theorems for a class of Bernstein-Durrmeyer operators preserving linear
functions, Ukrainian Math. J. 62 (2010), 913-922.
- [13] T. N. T. Goodman, A. Sharma, A modified Bernstein-Schoenberg operator, Proc. of the Conference on Constructive
Theory of Functions, Varna 1987 (ed. by Bl. Sendov et al.). Sofia: Publ. House Bulg. Acad. of Sci., 1988, 166-173.
- [14] M. Heilmann, F. Nasaireh, I. Ra¸sa, Complements to Voronovskaja’s formula, Chapter 11 In: D. Ghosh et al. (eds.),
Mathematics and Computing, Springer Proceedings in Mathematics & Statistics 253, Springer Nature Singapore
Pte Ltd. 2018, https://doi.org/10.1007/978-981-13-2095-8 11.
- [15] M. Heilmann, F. Nasaireh, I. Ra¸sa, Discrete Operators associated with Linking Operators, arXiv:1808.07239v1.
- [16] N. Ispir, On modified Baskakov operators on weighted spaces Turk. J. Math. 26(3) (2001), 355-365.
- [17] L.V. Kantorovich, Sur certain développements suivant les polynômes de la forme de S. Bernstein, I, II, C.R. Acad. URSS
563-568 (1930), 595-600.
- [18] A. Lupaş, The approximation by means of some linear positive operators, in Approximation Theory (M.W. Müller et al.,
eds), Akademie-Verlag, Berlin, 1995, 201-227.
- [19] A. Lupaş, Die Folge der Betaoperatoren, Dissertation, Universität Stuttgart, 1972.
- [20] L. Lupaş, A. Lupa¸s, Polynomials of Binomial Type and Approximation Operators, Studia Univ. Babe¸s-Bolyai, Mathematica,
XXXII, 4 (1987), 61-70.
- [21] D.H. Mache, Gewichtete Simultanapproximation in der Lp-Metrik durch das Verfahren der Kantorovic Operatoren, Dissertation,
Univ. Dortmund, 1991.
- [22] D.H. Mache, A link between Bernstein polynomials and Durrmeyer polynomials with Jacobi weights, In: Approx. Theory
VIII, Vol. 1: Approximation and Interpolation, Ch.K. Chui and L.L. Schmaker (Eds.), 403-410, World Scientific
Publ., 1995.
- [23] S.M. Mazhar, V. Totik, Approximation by modified Szász operators, Acta Sci. Math. 49 (1985), 257-269.
- [24] F. Nasaireh, I. Ra¸sa, Another look at Voronovskaya type formulas, Journal of Mathematical Inequalities, 12(1) (2018),
95-105.
- [25] F. Nasaireh, Voronovskaja-type formulas and applications, General Mathematics, 25(1-2) (2017), 37-43.
- [26] R. Paltanea, A class of Durrmeyer type operators preserving linear functions, Ann. Tiberiu Popoviciu Sem. Funct. Equat.
Approxim. Convex. (Cluj-Napoca) 5 (2007), 109-117.
- [27] I. Raşa, Discrete operators associated with certain integral operators, Stud. Univ. Babe¸s- Bolyai Math., 56(2) (2011),
537-544.
- [28] I. Raşa, E. Stanila, On some operators linking the Bernstein and the genuine Bernstein-Durrmeyer operators, J. Appl.
Funct. Anal. 9 (2014), 369-378.
- [29] D. D. Stancu, Asupra unei generalizari a polinoamelor lui Bernstein, Stud. Univ. Babes-Bolyai Math. 14 (1969), 31-45.
- [30] E. D. Stanila, On Bernstein-Euler-Jacobi Operators, Ph D Thesis, Duisburg-Essen University, July, 2014.
- [31] O. Szász, Generalization of S. Bernstein’s polynomials to the infinite interval J. Res. Natl. Bur. Stand. 45 (1950), 239-245.