Proving $\| g^{-1}-f^{-1}\|\leq 2\|{f^{-1}}\|^2\|g-f\|$
61484
Continuously invertible operators
61799
Prove that $\Vert f(b)-f(a)-f'(a)(b-a) \Vert\leq \sup_{x\in [a,b]} \Vert f''(x)\Vert\Vert b-a\Vert^2$
45219
Proving that $C$ is a subset of $f^{-1}[f(C)]$
19804
How to prove that $|w_{n+1}-w_n| \leq (2/3)^2 |w_n - w_{n-1}|$?
74202
Show that $|f(z_1)|=|f(z_2)|≤|z_1|^2=|z_2|^2$.
108995
Prove $|e^{i\theta} -1| \leq |\theta|$
56967
Show that $ f^2 − g^2 = C $ for some real constant C
70128
Prove that $(fg)^{(n)} = \sum_{k=0}^n \binom{n}{k}f^{(k)}(x)g^{(n-k)}(x)$
91085
how to find $|GL_2(F_p)|$
5526
Prove that $ℤ[i]^*= \{1,-1,i,-i\}$
154001
$(g\circ f)^{-1}=f^{-1}\circ g^{-1}$
127002
Prove that for a nonzero element $a$ of a field $F$ with $q$ elements $a^{-1} = a^{q-2}$
90343
Proving the inequality $|e^z-1|\leq e^{|z|}-1$
67291
Prove that there exists $n\in\mathbb{N}$ such that $f^{(n)}$ has at least n+1 zeros on $(-1,1)$
34323
Prove that $a^{(p-1)/2} \equiv 1$ (mod p) and $a^{(p-1)/2} \equiv -1 \pmod p$
138819
Prove that $\phi(n) \geq \sqrt{n}/2$
10859
Prove $\sup(f+g) \le \sup f + \sup g$