Abstract
This chapter is devoted to the study of those functions whose lower level sets are evenly convex, the so-called evenly quasiconvex functions. In Sect. 3.1 we define this class of functions, which provides greater minorants than the smaller class of the lower semicontinuous quasiconvex functions. Section 3.2 introduces the evenly quasiconvex hull providing the largest evenly quasiconvex minorant of a given function. Section 3.3 analyzes conjugates and subdifferentials for evenly quasiconvex functions, while Sect. 3.4 provides a sketch of quasiconvex duality theory. Finally, Sect. 3.5 describes an application in mathematical economy.
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