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Constructive notions of strict convexity
Author(s) -
Bridges Douglas S.
Publication year - 1993
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.19930390135
Subject(s) - convexity , constructive , mathematics , mathematical proof , mathematical economics , point (geometry) , relation (database) , preference relation , preference , calculus (dental) , computer science , geometry , statistics , economics , medicine , dentistry , process (computing) , database , financial economics , operating system
Two classically equivalent, but constructively inequivalent, strict convexity properties of a preference relation are discussed, and conditions given under which the stronger notion is a consequence of the weaker. The last part of the paper introduces uniformly rotund preferences, and shows that uniform rotundity implies strict convexity. The paper is written from a strictly constructive point of view, in which all proofs embody algorithms. MSC: 03F60, 90A06.