Abstract
Let F be a normed space and let B be a subspace of F. Assume that \( L\colon F\rightarrow L_{\infty }(\Omega )\), \(\Omega \subset \mbox{I\kern-.3468em R}^{m}\), is a linear bounded operator and M(L) = {f ∈ F : Lf ≥ 0 a.e. on Ω}. We establish some inequalities for best approximation of f ∈ M(L) by elements from B ∩ M(L). In the case when L is a differential operator and F is the Sobolev space \( W_{p}^{\ell }(\Omega )\) we obtain Jackson type estimates for simultaneous approximation of f ∈ M(L) by multivariate polynomials and entire functions of exponential type from M(L). This chapter relies on [75].
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Anastassiou, G.A. (2011). About L-Positive Approximations. In: Intelligent Mathematics: Computational Analysis. Intelligent Systems Reference Library, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17098-0_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-17098-0_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-17097-3
Online ISBN: 978-3-642-17098-0
eBook Packages: EngineeringEngineering (R0)