The Relation Between the Degree of Monotone Approximation and the Degree of Unconstrained Approximation

Abstract

Many researchers related to the degree of unconstrained approximation to  constrained approximation,  and proved the inequality: For a continuous  function  on a closed interval we have                                               

where  is a positive constant. The converse  of the relation  is not achieved, so we will obtain the converse  of the relation under some conditions on   which belonging to quasi normed spaces.