Abstract
Inequalities play an important role in Analysis, and since many inequalities are just convexity in disguise, we get that convexity is one of the most important tools in Analysis in general and not only in Convex Analysis. In this chapter we will introduce the notion of convexity in its various formulations, and we give some characterizations of convex functions and a few applications of convexity, namely, some classical inequalities as well as not so known inequalities.
All analysts spend half their time hunting through the literature for inequalities which they want to use but cannot prove. Harald Bohr
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Castillo, R., Rafeiro, H. (2016). Convex Functions and Inequalities. In: An Introductory Course in Lebesgue Spaces. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-30034-4_1
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