Convergence of a class of quartic interpolatory splines (Q1355422)

The existence and uniqueness of interpolatory quartic splines is investigated. The interpolatory function \(f\) is a 1-periodic locally integrable function defined on \([0,1]\). The unique existence of a 1-periodic quartic spline belonging to the class \(C^3[0,1]\) is proved which is a piecewise polynomial function of order 5 under the condition that the mean integral values of this spline and of the interpolatory function coincide in each subinterval of uniformly divided segment \([0,1]\). Using Meir and Sharma's method, the author obtains the estimates of norms with the help of the module of continuity of \(f'''\). We think that the author ought to explain the definitions of \(|\cdot|\) and \(w\) in the given context.