{"product_id":"on-the-shape-preserving-approximation-von-halgwrd-darwesh-und-eman-bhaya","title":"On The Shape Preserving Approximation","description":"\u003cp\u003eSometimes 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 \u0026gt; 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.\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783846524671\"\u003e\u003ch3\u003eConstrained and Unconstrained Approximation\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Softcover - 9783846524671","offer_id":39471350480989,"sku":"9783846524671","price":59.0,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/280bb8ff-1a16-4cb0-be73-130809ea900f.jpg?v=1773212072","url":"https:\/\/shop.autorenwelt.de\/products\/on-the-shape-preserving-approximation-von-halgwrd-darwesh-und-eman-bhaya","provider":"Autorenwelt Shop","version":"1.0","type":"link"}