Prove that there is a y that $f(y) = [f(x_1)+f(x_2)+ \cdots+ f(x_n) ]/ n$
69219
Prove there is a point $z\in[a,b]$ at which $f(z)=\frac{f(x_1)+f(x_2)+\cdots+f(x_k)}{k}$
77071
Solve the functional equation $f(xy) = f(x)f(y) - f(x + y) + 1$ and $f(1) = 2$
86367
Computing $f(x)$ if $\int_1^{xy} f(t) dt = y \int_1^x f(t) dt + x\int_1^y f(t) dt$ and $f(1) = 3$
27922
prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
109942
Find continuous functions such that $f(x+y)+f(x-y)=2[f(x)+f(y)]$
64457
Prove:$|x-1|+|x-2|+|x-3|+\cdots+|x-n|\geq n-1$
97104
Proof that continuous function on $ [0, 2]$ has $f(x) = f(x-1)$ for some $ x$
149354
Proof of continuity $f(x+y) = f(x) + f(y)$
1821
Proving $f(C) \setminus f(D) \subseteq f(C \setminus D)$ and disproving equality
27809
Find the function equation $f(x+f(y)+yf(x))=y+f(x)+xf(y)$
131692
How to show that $f_{0}f_{1}+f_{1}f_{2}+...+f_{2n-1}f_{2n} = f^{2}_{2n}$
122929
Prove that $Y=-2\sum_{i=1}^n \ln F_{X_i}(X_i)$ have distribution $\chi^2(2n)$
30688
Prove that $\frac{x_1}{1+x_2+x_3+\ldots+x_n}+\frac{x_2}{1+x_1+x_3+\ldots+x_n}+\ldots+\frac{x_n}{1+x_1+x_2+\ldots+x_{n-1}}\ge\frac{n}{2n-1}$.
152841
I want to show that $f(x)=x.f(1)$ where $f:R\to R$ is additive.
81921
If $f(x + y) = f(x) + f(y)$ showing that $f(cx) = cf(x)$ holds for rational $c$
68409
Consider $f(x,y)=\sup_{θ,φ}\{||e^{i θ }x+ e^{i φ }y||^2: θ,φ∈R\}$ in which $x,y\in\mathbb C^n$
133682
Prove that if $f(t)$ satisfies $f(t)=f'(t)$, then $f(t+s)=f(t)f(s)$ for all $t,s\in R$ without using the fact that $f(t)=c\cdot e^t$.