## Generalized convexity conesContents: Introduction The dual cone of C (psi sub 1,..., psi sub n) Extreme rays The cone dual to an intersection of generalized convexity cones Generalized difference quotients and multivariate convexity Miscellaneous applications of generalized convexity. |

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### Contents

CHAPTER TITLE PAGE | 10 |

EXTREME RAYS | 23 |

k THE CONE DUAL TO AN INTERSECTION OF GENERALIZED | 53 |

2 other sections not shown

### Common terms and phrases

C(tL Chapter conditions for f(x consider convex with respect convexity cones convexity of order Corollary corresponding cp(a cpn(x deduce defined Definition 3.1 Denote determinant difference quotients differential equation Differential Inequalities differential operators Dn_1 Doctor of Philosophy dp(t dp(x dual cone equivalent exists a point extreme rays following theorem function f(x fundamental system Furthermore Hence holds i-th column i=l i IL(b implies increasing function induction hypothesis inequality integration interpolation polynomial J=l J J Lagrange polynomial left hand side Leibniz's rule Lemma Let cp(x Let f(x linear combination n-1 sign changes Necessary and sufficient necessary condition necessity non-negative notation obtain ordinary convexity Pf(x positive functions positive measure Proof prove q.e.d. Remark result right continuous right hand side satisfies sequence sign changes signed measures sufficient conditions system of solutions Theorem 1.1 trivial measure un(x Wronskian Xn+1