On equivalent characterizations of convexity of functions

• Autores: Eleftherios Gkioulekas
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 44, Nº. 3, 2013, págs. 410-417
• Idioma: inglés
• DOI: 10.1080/0020739x.2012.703336
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• Resumen

  • detailed development of the theory of convex functions, not often found in complete form in most textbooks, is given. We adopt the strict secant line definition as the definitive definition of convexity. We then show that for differentiable functions, this definition becomes logically equivalent with the first derivative monotonicity definition and the tangent line definition. Consequently, for differentiable functions, all three characterizations are logically equivalent.