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On The Shape Preserving Approximation

 

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Sometimes one may desire to approximate a function defined on a finite interval (for example [-1,1]), subject to the conservation of so called shape properties (positivity, monotonicity and convexity). The first contribution is that we have approximated a function from a space Lp[-1,1], 0 > p, by a number of piecewise linear functions and we have obtained global estimate of each of them using the second order of Ditzian – Totik modulus of smoothness. Furthermore, these piecewise linear functions preserves the positivity of the function. Also proved the rate of coconvex approximation in the Lp[-1,1] spaces, in terms of the third order of Ditzian – Totik modulus of smoothness, where the constants involved depend on the location of the points of change of convexity. We have thus filled up a gap due to the uncertainty between previously known estimates involving the second order of Ditzian – Totik modulus of smoothness and the impossibility of having such estimates involving with the second order of usual modulus of smoothness.

Product Specifications
SKU :COC93617
AuthorHalgwrd Darwesh and Eman Bhaya
LanguageEnglish
BindingPaperback
Number of Pages128
Publishing Year2011-10-18T00:00:00.000
ISBN978-3846524671
Edition1 st
Book TypeMathematics
Country of ManufactureIndia
Product BrandLAP LAMBERT Academic Publishing
Product Packaging InfoBox
In The Box1 Piece
Product First Available On ClickOnCare.com2015-08-14 00:00:00
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