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.
|Author||Halgwrd Darwesh and Eman Bhaya|
|Number of Pages||128|
|Country of Manufacture||India|
|Product Brand||LAP LAMBERT Academic Publishing|
|Product Packaging Info||Box|
|In The Box||1 Piece|
|Product First Available On ClickOnCare.com||2015-08-14 00:00:00|