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Year 2019, Volume: 2 Issue: 2, 49 - 56, 01.06.2019
https://doi.org/10.33205/cma.506015

Abstract

References

  • [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.

On Geometric Series of Positive Linear Operators

Year 2019, Volume: 2 Issue: 2, 49 - 56, 01.06.2019
https://doi.org/10.33205/cma.506015

Abstract

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.

References

  • [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.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Radu Paltanea 0000-0002-9923-4290

Publication Date June 1, 2019
Published in Issue Year 2019 Volume: 2 Issue: 2

Cite

APA 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. June 2019;2(2):49-56. doi:10.33205/cma.506015
Chicago Paltanea, Radu. “On Geometric Series of Positive Linear Operators”. Constructive Mathematical Analysis 2, no. 2 (June 2019): 49-56. https://doi.org/10.33205/cma.506015.
EndNote Paltanea R (June 1, 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, vol. 2, no. 2, pp. 49–56, 2019, doi: 10.33205/cma.506015.
ISNAD Paltanea, Radu. “On Geometric Series of Positive Linear Operators”. Constructive Mathematical Analysis 2/2 (June 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, vol. 2, no. 2, 2019, pp. 49-56, doi:10.33205/cma.506015.
Vancouver Paltanea R. On Geometric Series of Positive Linear Operators. CMA. 2019;2(2):49-56.