افضل تقريب احادي الاتجاه لدوال غير مقيدة في الفضاء Lp,w (X) == The Best One Sided Approximation of Unbound ed Functions in Lp,w(X) Spaces
Author name:
علاء عدنان عواد المحمدي
Supervisor name:
صاحب كحيط جاسم الساعدي
General topic:
Mathematics
Specific topic:
Mathematics
Degree:
Doctorate
University:
Mustansiriyah University - College Of Science - Department Of Mathematics
Language:
English
University location:
Baghdad
First pages:
27T1166 - p.pdf
Abstract:
This thesis is devoted to approximation of unbounded functions and deals with what is called one - sided approximation by positive linear operators and entire functions in Approximation Theory. More precisely, the existence of a sequence of polynomials which lie above (or below) a given unbounded functions and approximate it arbitrary well have been investigating. Our offer an overview of this subject in the spaces , starting with the early works of Freud and ending by the latest results in this area. This branch of estimate degree of best one - sided approximation was studied in last 60 years and now contains a big variety of techniques and approaches. Our developed modified methods on one - sided approximation in the space and obtain several results.The degree of best one - sided approximation for unbounded functions in the space , by using Hermite - Fejer interpolation polynomials on [ - 1,1] and the interpolation polynomials on [ - , ] have been studied and founded.In addition, the estimation of best one - sided approximation in , by Valle - Poussin operator and Jackson's polynomial in terms average modulus have studied.Furthermore, an estimate of best one - sided approximation in weighted space by using Bernstein polynomial and by spline polynomials in terms the kth local modulus of - continuity and Ditzian - Totic modulus of smoothness are also proposed with details.The direct and inverse inequalities of best one sided approximation by entire functions are proved in space. Some conditions have been used to prove the relations between degree of best multi approximation and best one - sided multi approximation on interval ,as well as some results consisting direct and converse theorems for one - sided multi approximation in space on interval have been proved.
