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