Abstract
The purpose of this paper is to find the best multiplier approximation of unbounded functions in –space by using some discrete linear positive operators. Also we will estimate the degree of the best multiplier approximation in term of modulus of continuity and the averaged modulus.
Highlights
Here we will review some researchers who have studied the approximation of unbounded functions and who have obtained important results in this field, for example In (2015), S
Auad (2) estimated the degree of the best one –sided approximation of unbounded functions by using some discrete operator in Lp,ω-space. the researchers have studied the approximation of bounded functions and obtained important results
In this paper we will deal with unbounded functions by multiplier approximation and we shall use the Jackson polynomials and the Korovkin polynomials to find the best multiplier approximation of periodic unbounded functions in Lp,∅n(B), B = [0,2π] in terms of the modulus of continuity and the Averaged modulus
Summary
We will review some researchers who have studied the approximation of unbounded functions and who have obtained important results in this field, for example In (2015), S. K. Jassim and (1) studied the approximation of unbounded functions in locally –global space Lp,δ,ω(X).In(2015),S. Auad (2) estimated the degree of the best one –sided approximation of unbounded functions by using some discrete operator in Lp,ω-space (weighted space). the researchers have studied the approximation of bounded functions and obtained important results. (3) studied the approximation of bounded functions by de la vallee-poussin sums in weighted Orlicz spaces.Again in (2016),Sadigova ,S. (4) studied the approximation of bounded functions by Shifting operators in Morrey Type Space. First we introduce some definitions and some results that are used throughout this work. Definition 1 (5): A series ∑∞n=0 an is called a multiplier convergence if there is a Sequence
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