ON THE ERROR OF THE TWO-SIDES COMONOTONIC APPROXIMATION

Abstract

In this research, after finding some important definitions in the work, the approximation error preserving monotonicity on both sides was found, which represents the lower error and the upper error. Some of the properties of the weighted average modulus of smoothness.In this work, reference is made to the relationship between the modulus of smoothnessat interval lengths h^*_{r,s} and δ, r = 2, . . . , n. The best approximation between the polynomialand the weighting function f in the weighted space L_{w,q}(I), I = [-d, d] , 0 < q < 1.