On the q-Bernstein Polynomials

Abstract

We discuss here recent developments on the convergence of the q-Bernstein polynomials B(sub n)f which replaces the classical Bernstein polynomial with a one parameter family of polynomials. In addition, the convergence of iterates and iterated Boolean sum of q-Bernstein polynomial will be considered. Moreover a q-difference operator D(sub q)f defined by D(sub q)f = fX,QX is applied to q-Bernstein polynomials. This gives us some results which complement those concerning derivatives of Bernstein polynomials. It is shown that, with the parameter 0 is less than q is less than or equal to 1, if the change in k, f(sub r) is greater than or equal to 0 then D(k)(sub q)B(sub n)f is greater than or equal to 0. If f is monotonic so is D(sub q)B(sub n)f. If f is convex then D(2)(sub q)B(sub n)f is greater than or equal to 0.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2001
Accession Number
ADP013714

Entities

People

  • Halil Oruc
  • Necibe Tuncer

Organizations

  • Dokuz Eylül University

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Approximation (Mathematics)
  • Binomials
  • Boolean Algebra
  • Coefficients
  • Convergence
  • Identities
  • Interpolation
  • Mathematics
  • Numbers
  • Polynomials
  • Real Numbers
  • Sequences
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Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Graph Algorithms and Convex Optimization.
  • Linear Algebra