Convex interpolating splines of arbitrary degree. III

For given data (x _i, f_i) _i=0 ⁿ (x ₀<x ₁<...<x _n) we consider the possibility of finding a spline functions of arbitrary degreek (k3) with preassigned smoothnessl, where 1l(k-1)/2]. The splines should be such thats(x _i)=f _i (i=0, 1,...,n) ands is convex or nondecreasing and convex on x ₀,x _n]. An explicit formula for this function as well as the conditions that guarantee the required properties are established. An algorithm for the determination of the splines and the error bounds is also included.