Iterates of a class of discrete linear operators via contraction principle

Octavian Agratini; Ioan A. Rus

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 3, page 555-563
  • ISSN: 0010-2628

Abstract

top
In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

How to cite

top

Agratini, Octavian, and Rus, Ioan A.. "Iterates of a class of discrete linear operators via contraction principle." Commentationes Mathematicae Universitatis Carolinae 44.3 (2003): 555-563. <http://eudml.org/doc/249206>.

@article{Agratini2003,
abstract = {In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.},
author = {Agratini, Octavian, Rus, Ioan A.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {linear positive operators; contraction principle; weakly Picard operators; delta operators; operators of binomial type; linear positive operators; contraction principle; weakly Picard operators; delta operators; operators of binomial type},
language = {eng},
number = {3},
pages = {555-563},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Iterates of a class of discrete linear operators via contraction principle},
url = {http://eudml.org/doc/249206},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Agratini, Octavian
AU - Rus, Ioan A.
TI - Iterates of a class of discrete linear operators via contraction principle
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 3
SP - 555
EP - 563
AB - In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operators theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.
LA - eng
KW - linear positive operators; contraction principle; weakly Picard operators; delta operators; operators of binomial type; linear positive operators; contraction principle; weakly Picard operators; delta operators; operators of binomial type
UR - http://eudml.org/doc/249206
ER -

References

top
  1. Agratini O., Binomial polynomials and their applications in Approximation Theory, Conferenze del Seminario di Matematica dell'Universita di Bari 281, Roma, 2001, pp.1-22. Zbl1008.05010MR1850829
  2. Altomare F., Campiti M., Korovkin-Type Approximation Theory and its Applications, de Gruyter Series Studies in Mathematics, Vol.17, Walter de Gruyter, Berlin-New York, 1994. Zbl0924.41001MR1292247
  3. Cheney E.W., Sharma A., On a generalization of Bernstein polynomials, Riv. Mat. Univ. Parma (2) 5 (1964), 77-84. (1964) Zbl0146.08202MR0198074
  4. Kelisky R.P., Rivlin T.J., Iterates of Bernstein polynomials, Pacific J. Math. 21 (1967), 511-520. (1967) Zbl0177.31302MR0212457
  5. Lupaş A., Approximation operators of binomial type, New developments in approximation theory (Dortmund, 1998), pp.175-198, International Series of Numerical Mathematics, Vol.132, Birkhäuser Verlag Basel/Switzerland, 1999. MR1724919
  6. Mastroianni G., Occorsio M.R., Una generalizzatione dell'operatore di Stancu, Rend. Accad. Sci. Fis. Mat. Napoli (4) 45 (1978), 495-511. (1978) MR0549902
  7. Popoviciu T., Remarques sur les polynômes binomiaux, Bul. Soc. Sci. Cluj (Roumanie) 6 (1931), 146-148 (also reproduced in Mathematica (Cluj) 6 (1932), 8-10). (1931) Zbl0002.39801
  8. Rota G.-C., Kahaner D., Odlyzko A., On the Foundations of Combinatorial Theory. VIII. Finite operator calculus, J. Math. Anal. Appl. 42 (1973), 685-760. (1973) Zbl0267.05004MR0345826
  9. Rus I.A., Weakly Picard mappings, Comment. Math. Univ. Carolinae 34 (1993), 4 769-773. (1993) Zbl0787.54045MR1263804
  10. Rus I.A., Picard operators and applications, Seminar on Fixed Point Theory, Babeş-Bolyai Univ., Cluj-Napoca, 1996. Zbl1031.47035
  11. Rus I.A., Generalized Contractions and Applications, University Press, Cluj-Napoca, 2001. Zbl0968.54029MR1947742
  12. Sablonniere P., Positive Bernstein-Sheffer operators, J. Approx. Theory 83 (1995), 330-341. (1995) Zbl0835.41024MR1361533
  13. Stancu D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roumaine Math. Pures Appl. 13 (1968), 8 1173-1194. (1968) Zbl0167.05001MR0238001
  14. Stancu D.D., Occorsio M.R., On approximation by binomial operators of Tiberiu Popoviciu type, Rev. Anal. Numér. Théor. Approx. 27 (1998), 1 167-181. (1998) Zbl1007.41016MR1818225

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.