Landau-type extremal problem for the triple || f||∞,|| f′||p,|| f″||∞ on a finite interval Original Research Article

For any fixed finite interval I=[a,b] and any p, 1⩽p⩽∞, we prove that every extremal function to the problem|| f||L∞(I)⩽1, || f″||L∞(I)⩽4, || f′||Lp(I)→supis a perfect parabolic spline, whose extrema, excluding one at most, take the absolute value 1.