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Estimates for Comonotone Polynomial Approximation in
By Eman Samir Bhaya, Mathematics Department, College of Education,
Babylon University, Iraq.
Abstract
When we approximate a function f in which changes its monotonicity finitely many, say s time, in [0,1] , we wish some times that the approximatin polynomial follow these changes of monotonicity. However it is well known that this requireme restrict very much the degree of approximation that the polynomials can achieve, .
In [1] we proved that relaxing the comonotonicity requirements in very small intervals about the interior extremes and near the end points, what we called nearly comonotone approximation allows the polynomials to achieve a pointwise approximation rate . Also we proved that even when we relax the requirement of monotonicity of the polynomials on sets of measures approaching 0, is not reachable. We prove here that when f belongs to the Sobolev space, allow estimates involving the kth modulus of smoothness .
- وصف الــ Tags لهذا الموضوع
- comonotone approximation
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