Best multiplier Approximation in L_(p,∅_n ) (B)

Abstract

The purpose of this paper is to find best multiplier approximation of unbounded functions in L_(p,∅_n ) –space by using Trigonometric polynomials and by de la Vallee- Poussin operators. Also we will estimate the degree of the best multiplier approximation by Weighted –Ditzian-Totik modulus

Trigonometric Approximation by Modulus of Smoothness in Lp,α (X)

“…Let ∈ , ( ) , 1 ≤ < ∞ , ∈ + the modulus of smoothness ( , ) , is define by ( , ) , = |ℎ|≤ ‖∆ ℎ ( )‖ , , > 0 and have the following properties [3] ( 1 + 2 , ) , ≤ ( 1 , ) , + ( 2 , ) , with ( , ) , = 0 . For ∈ , ( ) , we define the -th derivative of f as function ( ) ∈ , ( ) satisfying…”

“…Here denote by ( ) , ( = 0,1, … ) the degree of best approximation of ∈ , ( ) by trigonometric polynomials of degree less than n , i.e., ( ) , = {‖ − ‖ , , ∈ } , where denotes the class of trigonometric polynomials of degree n The problems of approximation theory in the weighted and non-weighted space have been investigated in [1] and [6] weight respectively. The approximation problems by trigonometric polynomials in different spaces have been investigated by several authors see, for example, [3], [7], [8] and [9]. In this work we study the approximation problems of unbounded functions by trigonometric polynomials in the weighted space , ( ).…”