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01.11.2017 | Ausgabe 1-2/2017

Decisions in Economics and Finance 1-2/2017

Pseudoconvexity on a closed convex set: an application to a wide class of generalized fractional functions

Zeitschrift:
Decisions in Economics and Finance > Ausgabe 1-2/2017
Autor:
Laura Carosi

Abstract

The issue of the pseudoconvexity of a function on a closed set is addressed. It is proved that if a function has no critical points on the boundary of a convex set, then the pseudoconvexity on the interior guarantees the pseudoconvexity on the closure of the set. This result holds even when the boundary of the set contains line segments, and it is used to characterize the pseudoconvexity, on the nonnegative orthant, of a wide class of generalized fractional functions, namely the sum between a linear one and a ratio which has an affine function as numerator and, as denominator, the p-th power of an affine function. The relationship between quasiconvexity and pseudoconvexity is also investigated.

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