query: Real, bounded, convex function
positive_passages.docid: 9451
positive_passages.text: Show bounded and convex function on $\mathbb R$ is constant
negative_passages.docid: 74608
negative_passages.text: Convex function as supremum of countably many affine functions
negative_passages.docid: 144001
negative_passages.text: If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex
negative_passages.docid: 31548
negative_passages.text: Proof of "every convex function is continuous"
negative_passages.docid: 72908
negative_passages.text: Bounding a strange function
negative_passages.docid: 17408
negative_passages.text: An entire function whose real part is bounded must be constant.
negative_passages.docid: 14448
negative_passages.text: Elementary proof that $|x|^p$ is convex.
negative_passages.docid: 60887
negative_passages.text: $d_A(x) = \inf_{a \in A} \|x-a\|$ is convex if and only if $A$ is convex
negative_passages.docid: 2848
negative_passages.text: Convex integral inequality
negative_passages.docid: 116382
negative_passages.text: Showing convexity of a function with the restriction over an arbitrary line
negative_passages.docid: 97148
negative_passages.text: Does bounded variation imply boundedness
negative_passages.docid: 12556
negative_passages.text: A non-trivial, non-negative, function bounded below by its derivative with $f(0)=0$?
negative_passages.docid: 158399
negative_passages.text: Show that $\{(x_1,x_2):x_1x_2\geq4,x_1>0,x_2>0\}$ is a convex set
negative_passages.docid: 140083
negative_passages.text: Some questions about functions of bounded variation: Jordan's theorem
negative_passages.docid: 58988
negative_passages.text: Composition of convex function and affine function
negative_passages.docid: 120947
negative_passages.text: continuous real-valued function
negative_passages.docid: 54764
negative_passages.text: Given a real function $g$ satisfying certain conditions, can we construct a convex $h$ with $h \le g$?