query: Proving a function is a convex function
positive_passages.docid: 16943
positive_passages.text: Midpoint-Convex and Continuous Implies Convex
negative_passages.docid: 40905
negative_passages.text: Prove $f(\sum^k_{i=1} \alpha_i x_i) \leq \sum^k_{i=1} \alpha_i f(x_i) $ for a convex function f
negative_passages.docid: 2848
negative_passages.text: Convex integral inequality
negative_passages.docid: 138510
negative_passages.text: Show f(x) is a Lipschitz function
negative_passages.docid: 18763
negative_passages.text: injective holomorphic function on a convex set
negative_passages.docid: 73074
negative_passages.text: $f \text{ convex }\Rightarrow \forall (x_0,f(x_0))\in \Gamma(f) \exists a : \forall x\in \mathbb{R}, f(x) \ge a(x-x_0)+f(x_0)$
negative_passages.docid: 116382
negative_passages.text: Showing convexity of a function with the restriction over an arbitrary line
negative_passages.docid: 97584
negative_passages.text: How to prove this property using convexity?
negative_passages.docid: 27775
negative_passages.text: Proving a function is not a contraction
negative_passages.docid: 64866
negative_passages.text: Proving a Composition of Functions is Bijective
negative_passages.docid: 135867
negative_passages.text: $f(x)=x^3$ is convex nor concave without to derivate
negative_passages.docid: 123732
negative_passages.text: Proving that the maximum of two convex functions is also convex
negative_passages.docid: 25017
negative_passages.text: Why is every $p$-norm convex?
negative_passages.docid: 138457
negative_passages.text: Seminorms: Absolute Convexity
negative_passages.docid: 20614
negative_passages.text: Example of a function such that $\varphi\left(\frac{x+y}{2}\right)\leq \frac{\varphi(x)+\varphi(y)}{2}$ but $\varphi$ is not convex
negative_passages.docid: 25738
negative_passages.text: Jensen's Inequality implies convexity?
negative_passages.docid: 6335
negative_passages.text: Proving that the set enclosed by an ellipse is convex