Jan 14, 2017 · A different definition is that a function is convex iff its epigraph is convex. This is a visually intuitive definition, and it explains why we use the same word "convex" for both sets and functions.

May 14, 2018 · So, is there a way to distinguish convexity and strict convexity just by visual inspection of the graph of a function? And, if so, how? What can be the specific characteristic of a strict convex …

Oct 22, 2024 · In conclusion, how is the above definition related to my known 'definition' of a convex function using the second derivative, and what's better and more accurate about this definition?

It's more correct to say that he proved Jensen's Inequality (with arbitrary real weights) for functions which are midpoint convex and continuous. Of course, Jensen's Inequality with two arguments gives …

Jan 23, 2022 · In particular, why is "Convexity" so important, such that it (historically) made us interested in classifying functions as either Convex or Non-Convex? I found Roman J. Dwilewicz's A short …

Aug 16, 2019 · But if I have to check if a given function is convex or not, this definition seems hard and impractical to use. So, my question is, is there any easier way of checking convexity of a function …

Jan 23, 2021 · I noticed many identical questions on this site relating to equivalent definitions of convexity, see for example 668679, 740938, 318692, 1717542, 1761801, 3019331, 3047518 and …

Mar 16, 2014 · 0 Here is an attempt to make up for my ugly mistake on the strict convexity of Leontieff preferences ;). If I read you right, the guess you want to check is whether for complete, transitive and …

Apr 3, 2014 · Joint convexity means that the restriction of the function to any segment is a convex function of a single variable. Element-wise convexity means that only vertical and horizontal …

Jun 3, 2020 · There is a general topology flavoured definition of a general convexity space, which generalises the already existing notions of convexity that have been defined in the past.