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.
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