Convexity of Functions Produced by Bernstein Operators of Max-Product Kind
| Autor: | Ruo-Han Shen, Le-Yin Wei |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
TheoryofComputation_MISCELLANEOUS
Pure mathematics Property (philosophy) Continuous function Applied Mathematics 010102 general mathematics Regular polygon Mathematical properties 01 natural sciences Bernstein polynomial Convexity 010101 applied mathematics Mathematics (miscellaneous) Product (mathematics) Constant function 0101 mathematics Mathematics |
| Zdroj: | Results in Mathematics. 74 |
| ISSN: | 1420-9012 1422-6383 |
| Popis: | Bernstein polynomials have nice mathematical properties and wide applications in various fields. An interesting property which is very useful in computer-aided design is preservation of convexity of functions. These polynomials have been extended in various forms according to different applications. One form considered in this paper is the family of Bernstein operators of max-product kind. These nonlinear operators have many interesting properties including preservation of quasiconvexity of functions, but do not preserve convexity of linear functions. In this paper we strengthen this observation for the linear functions. We show that for any continuous function with nonnegative values, the functions generated by Bernstein operators of max-product kind are not convex unless they are constant functions. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full text from SpringerLink