ABSTRACT

Since a function f is quasi-convex in a domain D ∈ R n $ D\in { \mathbb R }^n $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315202259/e12d0279-bd94-4c37-8da4-db82a118a772/content/inline-math7_1.tif"/> , iff ( - f ) $ (-f) $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315202259/e12d0279-bd94-4c37-8da4-db82a118a772/content/inline-math7_2.tif"/> is quasi-concave in that domain, we can repeat most of the results of the previous chapter by replacing the upper-level set by the lower-level set, the ≥ $ \ge $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315202259/e12d0279-bd94-4c37-8da4-db82a118a772/content/inline-math7_3.tif"/> sign by ≤ $ \le $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315202259/e12d0279-bd94-4c37-8da4-db82a118a772/content/inline-math7_4.tif"/> , and the operation ‘min’ by ‘max’. However, there are some useful and interesting results in quasi-convex function theory, and we will risk some repetition and provide all relevant information on the topic.