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

In this paper, we prove the existence of common random fixed point for two random operators under general quasi contraction condition in a complete pnormed space X (with whose dual separates the point of X). Also, the wellposedness problem of random fixed points is studied. Our results essentially cover special cases.

The main objective of this article is to study the degree of best one-sided multiplier approximation of unbounded functions ,( ),[ 1,1]npgLY Y= −by means of the average modulus of smoothness by using sequences of algebraic polynomials Pn of degree less than n, nr+ 1, also in this search we shall prove a direct theorem by sequences Pn and some results.

The aim of studying this research is to find the best one-sided multiplier approximation of unbounded function in 퐿푝,휓푛(푋)−space,푋=[0,1],푝≥1by using type of operators 하푛(푓),픾풏(푓)by means of operators of algebraic polynomials as well as to show the relationship between the multiplier averaged modules of smoothness (휏-modules) and variation of unbounded functions in퐿푝,휓푛(푋)−spac

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