New theorems in approximation theory

Abstract EN

The aim of this paper is to prove some results for equivalence of moduli of smoothnes in approximation theory , we used a"non uniform" modulus of smoothness and the weighted Ditzian –Totik moduli of smoothness in by spline functions ,several results are obtained .For example , it shown that ,for any the inequality , is satisfied ,finally, similar result for chebyshev partition and weighted Ditzian –Totik moduli of smoothness are also obtained.

Key words: Univariate splines , moduli of smoothness , "non uniform" modulus of smoothness , weighted Ditzian –Totik moduli of smoothness.