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Abstract Convex Analysis

Ivan Singer

ISBN: 978-0-471-16015-1 August 1997 491 Pages


This book examines abstract convex analysis and presents the results of recent research, specifically on parametrizations of Minkowski type dualities and of conjugations of type Lau. It explains the main concepts through cases and detailed proofs.
Abstract Convexity of Elements of a Complete Lattice.

Abstract Convexity of Subsets of a Set.

Abstract Convexity of Functions on a Set.

Abstract Quasi-Convexity of Functions on a Set.

Dualities Between Complete Lattices.

Dualities Between Families of Subsets.

Dualities Between Sets of Functions.


v-Dualities and _|_-Dualities.

Abstract Subdifferentials.

Notes and Remarks.