query: Proof for convexity of a function
positive_passages.docid: 16943
positive_passages.text: Midpoint-Convex and Continuous Implies Convex
negative_passages.docid: 115930
negative_passages.text: Is every convex function on an open interval continuous?
negative_passages.docid: 86643
negative_passages.text: Convex function almost surely differentiable.
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: 116851
negative_passages.text: Show that f(x) is convex
negative_passages.docid: 597
negative_passages.text: f is differentiable on convex domain D and Re(f')>0 implies f is injective on D
negative_passages.docid: 49783
negative_passages.text: A possible inequality related to binomial theorem (or, convex/concave functions)
negative_passages.docid: 150727
negative_passages.text: Characterization convex function.
negative_passages.docid: 123732
negative_passages.text: Proving that the maximum of two convex functions is also convex
negative_passages.docid: 102959
negative_passages.text: Show that $f$ is convex if and only if $f\left( \sum_{i=1}^m\lambda_ix_i \right) \leq \sum_{i=1}^m\lambda_if(x_i)$
negative_passages.docid: 66151
negative_passages.text: Solving inequality for convex functions.
negative_passages.docid: 95293
negative_passages.text: Proof that $|\sqrt{x}-\sqrt{y}| \leq \sqrt{|x-y|},\quad x,y \geq 0$
negative_passages.docid: 116382
negative_passages.text: Showing convexity of a function with the restriction over an arbitrary line
negative_passages.docid: 82198
negative_passages.text: Proving Convexity of Multivariate Function using Conditional Univariate Convexity
negative_passages.docid: 2848
negative_passages.text: Convex integral inequality
negative_passages.docid: 101690
negative_passages.text: Is linear function convex or concave?
negative_passages.docid: 52231
negative_passages.text: Prove or disprove {$\sum_{i=1}^n x_i^2 = 1$} is convex