query: Existence of a Functional Equation
positive_passages.docid: 98255
positive_passages.text: Find $f(x)$ such that $f(f(x)) = x^2 - 2$
negative_passages.docid: 35281
negative_passages.text: $1992$ IMO Functional Equation problem
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: 62111
negative_passages.text: Functional Equation $f(mn)=f(m)f(n)$.
negative_passages.docid: 25953
negative_passages.text: Solving a functional relation $f\left( x \cdot f(y)\right)=x^2 \cdot y^a$
negative_passages.docid: 47212
negative_passages.text: Solving functional equation
negative_passages.docid: 137971
negative_passages.text: Existence of an holomorphic function
negative_passages.docid: 65418
negative_passages.text: Solve these functional equations: $\int_0^1\!{f(x)^2\, \mathrm{dx}}= \int_0^1\!{f(x)^3\, \mathrm{dx}}= \int_0^1\!{f(x)^4\, \mathrm{dx}}$
negative_passages.docid: 90435
negative_passages.text: Prove that there exist linear functionals $L_1, L_2$ on $X$
negative_passages.docid: 104209
negative_passages.text: Functional equation - Cyclic Substitutions
negative_passages.docid: 88683
negative_passages.text: Functional equation $f\left(\frac{x+y}{2}\right)+f\left(\frac{2xy}{x+y}\right)=f(x)+f(y)$ implies $2f(\sqrt{xy})=f(x)+f(y)$
negative_passages.docid: 76148
negative_passages.text: Show that $\exists c \in \mathbb{R} : f(c) = 0$
negative_passages.docid: 144090
negative_passages.text: How to solve the functional equation $f\left(x^2+f(y)\right)=y+f(x)^2$
negative_passages.docid: 150005
negative_passages.text: Existence of points in a differentiable function
negative_passages.docid: 17343
negative_passages.text: Function on $[a,b]$ that satisfies a Hölder condition of order $\alpha > 1 $ is constant
negative_passages.docid: 101852
negative_passages.text: Differential equations that are also functional
negative_passages.docid: 148247
negative_passages.text: Prove the existence of an analytic function