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.

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

This research focused on finding a mathematical space, extending to the Lebesgue spaces, through which it is possible to get the approximation for unbounded functions depending on the fundamental theory of approximation (Korvkein Theorem) using some linear operators Depending on the averaged modulus of smoothness of order k (τ-modulus).

The purpose of this paper is to find best multiplier approximation of unbounded functions in L p,ϕm –space by q-Bernstein-Kantorovich Aperator, in terms of the modulus of smoothness of one order using Korevkin Theorem.