• ON BEST ONE-SIDED APPROXIMATION BY THREE MONOTONE SPLINES IN WEIGHTED SPACES

Abstract

Degree of best one-sided approximation of a function which lies in space of 3-monotone continuous function on i.e. is such that its third divided difference are nonnegative for all choices of distinct points in by construct an operator which dependents on constructed spline of minimal defect (i.e. with equidistant knot in ), which is also 3-monoton , is studied in this work. The result which we end in it that the degree of best one-sided approximation of a function is minimized by using the above operator which dependent on the spline that satisfies: