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Guerraggio, Angelo; Molho, Elena

The origins of quasi-concavity: a development between mathematics and economics. (English) Zbl 1102.01021

Hist. Math. 31, No. 1, 62-75 (2004).
Summary: The origins of the notion of quasi-concave function are considered, with special interest in some work by John von Neumann, Bruno de Finetti, and W. Fenchel. The development of such pioneering studies subsequently led to a whole field of research, known as “generalized convexity.” The different styles of the three authors and the various motivations for introducing quasi-concavity are compared, without losing sight of economic applications characteristic of the whole field of generalized convexity.

Cited in 21 Documents

MSC:

01A60 History of mathematics in the 20th century
52A01 Axiomatic and generalized convexity
90C26 Nonconvex programming, global optimization
91A10 Noncooperative games
91B16 Utility theory

Keywords:

Convexity; Quasi-convexity; utility theory; von Neumann; de Finetti; Fenchel
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References:

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