Support-type properties of convex functions of higher order and Hadamard-type inequalities
نویسندگان
چکیده
منابع مشابه
Support–type Properties of Convex Functions of Higher Order and Hadamard–type Inequalities
It is well–known that every convex function f : I → R (where I ⊂ R is an interval) admits an affine support at every interior point of I (i.e. for any x0 ∈ Int I there exists an affine function a : I → R such that a(x0) = f(x0) and a ≤ f on I). Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree no greater than th...
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 2007
ISSN: 0022-247X
DOI: 10.1016/j.jmaa.2006.11.011