[1] U. Abel, Geometric series of Bernstein-Durrmeyer operators, East J. on Approx. Vol. 15, No. 4 (2009) 439–450.
[2] U. Abel, M. Ivan, R. Paltanea, Geometric series of Bernstein operators revisited, J. Math. Anal. Appl. Vol. 400. No. 1
(2013) 22-24.
[3] U. Abel, M. Ivan, R. Paltanea, Geometric series of positive linear operators and the inverse Voronovskaya theorem on a
compact interval, J. Approx. Theory Vol. 184 (2014), 163-175.
[4] F. Altomare, S. Diomede, Asymptotic formulae for positive linear operators: direct and converse results, Jaen J. Approx.
Vol. 2, No. 2 (2010) 255–287.
[5] J. Bustamante, Bernstein Operators and Their Properties, Birkhäuser, 2017.
[6] R. A. DeVore, G. G. Lorentz, Constructive approximation, Springer, Berlin, 1993.
[7] H Gonska, R. Paltanea, General Voronovskaja and asymptotic theorems in simultaneous approximation, Mediterranean
J. Math. Vol. 7 (2010) 37-49.
[8] V. Gupta, G. Tachev, Approximation with Positive Linear Operators and Linear Combinations, Springer, 2017.
[9] G. G. Lorenz, Bernstein polynomials, Univ. Toronto Press, 1953.
[10] R. Paltanea, Approximation Theory Using Positive Linear Operators, Birkhäuser, Boston, 2004.
[11] R. Paltanea, The power series of Bernstein operators, Automation Computers Applied Mathematics Vol. 15, No. 1
2006, 7-14.
[12] I. Raşa, Power series of Bernstein operators and approximation resolvents Mediterr. J. Math. Vol. 9 (2012) 635-644.
[13] I. A. Rus, Iterates of Bernstein operators, via contraction principle, J. Math. Anal. Appl. Vol 292, No. 1 (2004) 259-261.
We study the existence and the norm of operators obtained as power series of linear positive operators with particularization to Bernstein operators. We also obtain a Voronovskaja-kind theorem.
[1] U. Abel, Geometric series of Bernstein-Durrmeyer operators, East J. on Approx. Vol. 15, No. 4 (2009) 439–450.
[2] U. Abel, M. Ivan, R. Paltanea, Geometric series of Bernstein operators revisited, J. Math. Anal. Appl. Vol. 400. No. 1
(2013) 22-24.
[3] U. Abel, M. Ivan, R. Paltanea, Geometric series of positive linear operators and the inverse Voronovskaya theorem on a
compact interval, J. Approx. Theory Vol. 184 (2014), 163-175.
[4] F. Altomare, S. Diomede, Asymptotic formulae for positive linear operators: direct and converse results, Jaen J. Approx.
Vol. 2, No. 2 (2010) 255–287.
[5] J. Bustamante, Bernstein Operators and Their Properties, Birkhäuser, 2017.
[6] R. A. DeVore, G. G. Lorentz, Constructive approximation, Springer, Berlin, 1993.
[7] H Gonska, R. Paltanea, General Voronovskaja and asymptotic theorems in simultaneous approximation, Mediterranean
J. Math. Vol. 7 (2010) 37-49.
[8] V. Gupta, G. Tachev, Approximation with Positive Linear Operators and Linear Combinations, Springer, 2017.
[9] G. G. Lorenz, Bernstein polynomials, Univ. Toronto Press, 1953.
[10] R. Paltanea, Approximation Theory Using Positive Linear Operators, Birkhäuser, Boston, 2004.
[11] R. Paltanea, The power series of Bernstein operators, Automation Computers Applied Mathematics Vol. 15, No. 1
2006, 7-14.
[12] I. Raşa, Power series of Bernstein operators and approximation resolvents Mediterr. J. Math. Vol. 9 (2012) 635-644.
[13] I. A. Rus, Iterates of Bernstein operators, via contraction principle, J. Math. Anal. Appl. Vol 292, No. 1 (2004) 259-261.
Paltanea, R. (2019). On Geometric Series of Positive Linear Operators. Constructive Mathematical Analysis, 2(2), 49-56. https://doi.org/10.33205/cma.506015
AMA
Paltanea R. On Geometric Series of Positive Linear Operators. CMA. Haziran 2019;2(2):49-56. doi:10.33205/cma.506015
Chicago
Paltanea, Radu. “On Geometric Series of Positive Linear Operators”. Constructive Mathematical Analysis 2, sy. 2 (Haziran 2019): 49-56. https://doi.org/10.33205/cma.506015.
EndNote
Paltanea R (01 Haziran 2019) On Geometric Series of Positive Linear Operators. Constructive Mathematical Analysis 2 2 49–56.
IEEE
R. Paltanea, “On Geometric Series of Positive Linear Operators”, CMA, c. 2, sy. 2, ss. 49–56, 2019, doi: 10.33205/cma.506015.
ISNAD
Paltanea, Radu. “On Geometric Series of Positive Linear Operators”. Constructive Mathematical Analysis 2/2 (Haziran 2019), 49-56. https://doi.org/10.33205/cma.506015.
JAMA
Paltanea R. On Geometric Series of Positive Linear Operators. CMA. 2019;2:49–56.
MLA
Paltanea, Radu. “On Geometric Series of Positive Linear Operators”. Constructive Mathematical Analysis, c. 2, sy. 2, 2019, ss. 49-56, doi:10.33205/cma.506015.
Vancouver
Paltanea R. On Geometric Series of Positive Linear Operators. CMA. 2019;2(2):49-56.