التقريب المقيد على الفضاءات المرتبة == Constrained Approximation on Ordered Spaces
Author name:
ولاء حسين احمد الموسوي
Supervisor name:
ايمان سمير عبد علي بهية
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Master
University:
University of Babylon - College Of Education For Pure Sciences - Department Of Mathematics
Language:
English
University location:
Babylon
First pages:
27T1028 - p.pdf
Abstract:
Our work concerns itself with the constrained approximation of functions in L_p space for 0<p<1 with values in an ordered spaces.For maps on [ - 1,1] with values in ordered space we define a quasi - norm, then in terms of this norm we define versions of k - th moduli of smoothness and K - functionals.First we prove direct theorem for convex shape preserving approximation of functions on [ - 1,1] with values in an ordered space. As a direct consequence of the convex approximation direct theorem we get a direct theorem for monotone shape preserving approximation.For a piecewise convex function in L_p^k [ - 1,1] we also introduce a direct coconvex approximation theorem in the r - fold L_p space.For function of values in an ordered space we introduce an equivalence between the k - modulus of smoothness and k - functionals , that we defined above.Using this relation we introduce direct theorem for k - monotone approximation of functions defined on [0,1] and of values in an ordered space. In addition to these results, we also introduce a direct theorem in terms of k - functional operator.As a direct corollary we also obtained a direct theorem using Bernstein operator.As an application in the approximation field we approximate functions in L_p space, 0<p<1 of values in an ordered set using radial basis function neural networks, in terms of the k - th order modulus of smoothness
