Constrained Spline approximation

Abstract EN

In this paper, we find the relationships between the order of constrained approximation by a polynomials which is copositive with a function (?), by modulus of smoothness ??−1 , to the function ?́ ,which is multiply by ?? , and between the best approximation to the pairs of "intertwining splines of a polynomials" in ?=[−?,?] , and the same of relationships but by the modulus of smoothness ??−1? to the function ?́ multiply by ?−1 |??| .

Also we find the order of constrained approximation to the pairs of intertwining polynomials in ( ??⋃??+1 ) .