On the degree of approximation by linear positive operators
โ Scribed by B Mond
- Publisher
- Elsevier Science
- Year
- 1976
- Tongue
- English
- Weight
- 111 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0021-9045
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## Abstract A unified class of linear positive operators has been defined. Using these operators some approximation estimates have been obtained for unbounded functions. For particular linear positive operators these results sharpen and improve the earlier estimates due to Fuhua Cheng (J. Approx. T
The degree of approximation in L p -spaces by positive linear operators is estimated in terms of the integral modulus of smoothness. It is shown that the conjectured optimal degree of approximation is not attained in the class of functions having a second derivative belonging to L p .
We consider the problem of multivariate convex approximation by positive linear operators. Let E be a k-dimensional compact convex set in R k with k 2, 0/R k an open set containing E, and let L: C(E ) ร C 1 (0) be a positive linear operator. Our main result of this paper shows that if L preserves co