Vol. 98, No. 1, 1982

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A geometric characterization of nth order convex functions

Antonio Granata

Vol. 98 (1982), No. 1, 91–98
Abstract

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
Milestones
Received: 9 July 1980
Published: 1 January 1982
Authors
Antonio Granata