In this work, the direct theorems of unrestrained mappings via some linear operators in terms of Ditzian-Totik and module of continuity have been considered and we got the best approximation by arriving at , approximate these functions via a piecewise constant function, used Minkowski’s inequality and employing certain algebraic polynomials on closed intervals. The direct approximation co-positive theorems for unbounded functions have also been demonstrated. Moreover, The distinguishing features of this paper over previous papers are finding unconstrained functions in space and their rapid approximation with minimal error using algebraic polynomials.