NOTE ON THE ITERATES OF q- AND (p,q)-BERNSTEIN OPERATORS

In this note we are concerned with the limit behavior of the iterates of q and (p,q)-Bernstein operators. The convergence of the iterates of q-Bernstein operators was proved by H. Oruç and N. Tuncer in 2002 and by X. Xiang, Q. He and W. Yang in 2007, using the q-differences, Stirling polynomials and...

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Bibliographic Details
Published inScientific Studies and Research Vol. 26; no. 2
Main Author VOICHIŢA, ADRIANA RADU
Format Journal Article
LanguageEnglish
Published Bacau Universitatea "Vasile Alecsandri" din Bacau 01.07.2016
Subjects
Convergence
Eigenvalues
Operators
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Summary:In this note we are concerned with the limit behavior of the iterates of q and (p,q)-Bernstein operators. The convergence of the iterates of q-Bernstein operators was proved by H. Oruç and N. Tuncer in 2002 and by X. Xiang, Q. He and W. Yang in 2007, using the q-differences, Stirling polynomials and matrix techniques and by S. Ostrovska in 2003, with the aids of eigenvalues. We try to prove the convergence from some different points of view: using contraction principle (Weakly Picard Operators Theory). The theory of (weakly) Picard operator is very useful to study some properties of the solutions of those equations for which the method of successive approximations works.
ISSN:2067-3566
2457-497X