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Characterizations of $$r$$-convex functions. (English) Zbl 1231.90314
Summary: This paper discusses some properties of $$r$$-convexity and its relations with some other types of convexity. A characterization of convex functions in terms of $$r$$-convexity is given without assuming differentiability. The concept of strict $$r$$-convexity is introduced. For a twice continuously differentiable function $$f$$, it is shown that the strict $$r$$-convexity of $$f$$ is equivalent to a certain condition on $$\nabla ^{2} f$$. Further, it is shown that this condition is satisfied by quasiconvex functions satisfying a less stringent condition.

##### MSC:
 90C25 Convex programming
Full Text:
##### References:
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