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A
geometric characterization of nth order convex functions
Antonio Granata |
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Vol. 98 (1982), No. 1, 91–98
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Abstract |
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A new geometric characterization is presented for a function convex of order n on an open interval, distinct from the whole of R. We shall prove that if f : (a,b) → R with b < +∞, if α is an arbitrarily fixed number, α ≧ b, and if F(x) denotes the ordinate of the point of intersection in the x,y-plane between the vertical line x = α and the osculating parabola of order n to the graph of f at the point (x,f(x)), then f is convex of order n on (a,b) iff F is increasing thereon. |
Mathematical Subject Classification 2000
Primary: 26A51
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Milestones
Received: 9 July 1980
Published: 1 January 1982
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Authors |
| Antonio Granata | |
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