# functional

1. ### functional equation

If a function f satisfies the relation f(x)f''(x)-f(x)f'(x)=(f'(x))^2\,\forall x \in\mathbb{R} and f(0)=f'(0)=1, then value of f(x) is .
2. ### Functional Equation

How to solve the equation ? f(x)=\sqrt{f(x^2 )} .
3. ### A functional equation

Hello all, Resolve the functional equation f(x^n-i\sqrt2)+f(x^n)+f(x^n+i\sqrt2)=a+bi where i^2=-1 , n\in \mathbb N* and a,b\in \mathbb R. All the best, Integrator
4. ### Deriving the constant acceleration formulas using functional notation.

Hi, So I was trying to develop a more in-depth understanding of the constant acceleration equations, especially v^2 = u^2+2as. I found a video showing the derivation of this formula: JnFykw00HvE His logic goes like this. 1: Acceleration is the derivative of velocity w.r.t. time. a = dv/dt...
5. ### Functional equation

f(nx)=[fâ€™(x) ]^{n} \; \; , x\in \mathbb{R} , n>0 . f(x)=?
6. ### Need help with a functional equation

$$f: \mathbb{R} \to \mathbb{R}\qquad \frac{f(x+y)}{x+y} = \frac{f(x)-f(y)}{x-y}, \qquad \forall x,y\in \mathbb{R}, \left|x\right| \neq \left|y\right|$$ Can I prove anything interesting about this function? I need to find it.

Hello
8. ### Calculate the derivative of a functional.

How to calculate the $J'\left(y\right)$ of $J\left(y\right) = \int_0^1 g\left( y\left( x \right) \right) \operatorname dx$ ? It will be useful if can provide the derivation procss.
9. ### Functional Equation

How to solve the equation ? f(x+y)=f(x)f(y)
10. ### Functional equation

Z(\frac{x+y}{2})=\frac{Z(x)+Z(y)}{2}
11. ### Functional analysis

in a normed space V can any proper W subspace be an open in V?
12. ### Another functional disfunction

If r(t) = 2t+3 and s(t) = 7t^2 - t find :- s(r(t)) s(r(t)) = s(2t + 3) = 7(2t + 3)^2 âˆ’ (2t + 3) <<<{Where is this guy coming from?} = 7(4t^2 + 12t + 9) âˆ’ (2t + 3) = (28t^2 + 84t + 63) âˆ’ (2t + 3) = 28t^2 + 82t + 60 I can understand the first (2t + 3)^2 but surely that should cover...
13. ### Functional misunderstanding

Hi guys I'm just struggling with a few things in my maths revision. Wondering if one of you geniuses could give me a kick in the right direction. Given the function f(t) = 2t^2 + 4 find 1. f(4x+2) f(4x + 2) = 2(4x + 2)^2 + 4 = 2(16x^2 + 16x + 4) + 4 = 32x^2 + 32x + 8 + 4 = 32x^2 + 32x + 12...
14. ### Functional analysis Linear bdd operator helppppppp

Let A:X \to l^\infty be a linear bounded operator from a normed space X to l^\infty . Show that there is a bounded sequence of bounded functionals \{f_n\}_{n=1}^{\infty} \subset X' such that Ax=(f_n(x))_{n=1}^{\infty}. Moreover, \|A\|=sup\|f_n\|
15. ### The 2nd Int'l Conference on Functional Analysis (ICFA 2016)

The 2nd Int'l Conference on Functional Analysis (ICFA 2016) The 2nd Int'l Conference on Functional Analysis 2016.7.25-27 Suzhou Topics HilbertSpaces BanachSpaces Banach-SteinhausTheorem Hahn-BanachTheorem OpenMappingTheorem ClosedGraphTheorem...
16. ### Functional DE

Determine all pairs of differentiable functions and constants $(f(x),R)$ where $f:\mathbb R\to\mathbb R$ and $R\in\mathbb R$ such that $f'(x)=Rf(x+1)$. So far I have found $(0, 0)$, $(Ce^x, 1/e)$, and $(Cxe^x, 1/e)$. I was wondering if there are any more, or how to find all possible...
17. ### Measurable solutions to a functional equation

Hello, I am studying a simple stochastic two-player game and I got stuck on the following issue. Is this statement true? Let c > 0, \beta \in (0,1), let Y \sim U[0,1], and let \mathbb{I} be the indicator function. Then there exists a bounded measurable solution \$v : [0,1] \rightarrow...
18. ### A functional equation

Hello, To solve the functional equation f(x+f(x))=x^2+2x+3.
19. ### Variational problem: quadratic functional

Let me bring to your attention the following problem. Suppose we have the functional F = \int\limits_{a}^{b} f(y(x))\cdot(\frac{dy}{dx})^2 dx with differential constraint \frac{dy}{dx} / n(y(x)) - 1 = 0 - DE. We write the Lagrangian for this problem L =...
20. ### Differential equations and functional minimum

Hi, it can be shown that for some operators A (ie argument of A is a function) solving the equation A(u)=f (u is unknown function, f is known (given) function) is equivalent with finding minimum of some functional F (ie F is operator with function as an argument and with values from real...