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Positive Operators

q -Bernstein polynomials and their iterates

Convergence of Generalized Bernstein Polynomials

http://web.deu.edu.tr/halil.oruc/qbernsteinbeziercam.pdf

q -Bernstein polynomials and Bézier curves

We propose the concept of ordered weighted averaging (OWA) generation function with some properties, illustrative examples, and usages. A number of new properties of OWA operators and relations between some well-known OWA operators are proposed and proved using OWA Generation Functions. We discuss some orness/andness adjustment methods for a predetermined OWA operator. A practical application about investment prediction problem is given with detailed illustration and analysis, which can show the advantages of the adjustment methods proposed in this paper. In particular, the concept consistent adjustment matrix is proposed and the interests and advantages of it can be shown by its special properties.

OWA Generation Function and Some Adjustment Methods for OWA Operators With Application

This paper is concerned with a generalization of the classical Bernstein polynomials where the function is evaluated at intervals which are in geometric progression. It is shown that, when the function is convex, the generalized Bernstein polynomials Bn are monotonic in n, as in the classical case.

/pdf/a-generalization-of-the-bernstein-polynomials-39j7ryuxvf.pdf

A generalization of the Bernstein polynomials

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A generalization of the Bernstein polynomials