Newbetuts

If $f:[a,b]\to \mathbb{R}$ satisfies $|f'(x)|<1, \forall x\in [a,b]$, is $f$ necessarily a contraction?

Why does Rudin define $k = \frac{y^n-x}{n y^{n-1}}$ or $h < \frac{x - y^n}{n(y+1)^{n-1}}$ when he tries to prove that every real x has a nth root?

Between any two continuous functions $f>g$, can we find a real-analytic function?

Is there any way to systematically do all epsilon delta proofs?

$L^p$-space is a Hilbert space if and only if $p=2$

Is there a simpler proof of this fact in analysis?

Compute this integral

Is it possible to turn infinite sums into infinite products?

Prove that every isometry on $\mathbb{R}^2$ is bijective

What are the integrals defined for $\mathbb{R}^n$?

Characterization of real functions which have limit at each point

How to show that $(1+\frac1x)^x$ is increasing on $[0,+\infty[$

Is there any proof for this formula $\lim_{n \to \infty} \prod_{k=1}^n \left (1+\frac {kx}{n^2} \right) =e^{x/2}$?

Proving measurable function: Real versus rational number [duplicate]

Smoothest function which passes through given points?

Smoothness of harmonic functions

separately continuous functions $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ but nowhere continuous

Interchanging Summation and Integral

New posts in real-analysis

If $f:[a,b]\to \mathbb{R}$ satisfies $|f'(x)|<1, \forall x\in [a,b]$, is $f$ necessarily a contraction?

average of maximal function is less than its infimum?

Show that $f$ is a polynomial if it's the uniform limit of polynomais

Why does Rudin define $k = \frac{y^n-x}{n y^{n-1}}$ or $h < \frac{x - y^n}{n(y+1)^{n-1}}$ when he tries to prove that every real x has a nth root?

Between any two continuous functions $f>g$, can we find a real-analytic function?

Is there any way to systematically do all epsilon delta proofs?

$L^p$-space is a Hilbert space if and only if $p=2$

Is there a simpler proof of this fact in analysis?

Compute this integral

Is it possible to turn infinite sums into infinite products?

Prove that every isometry on $\mathbb{R}^2$ is bijective

What are the integrals defined for $\mathbb{R}^n$?

Characterization of real functions which have limit at each point

How to show that $(1+\frac1x)^x$ is increasing on $[0,+\infty[$

Is there any proof for this formula $\lim_{n \to \infty} \prod_{k=1}^n \left (1+\frac {kx}{n^2} \right) =e^{x/2}$?

Proving measurable function: Real versus rational number [duplicate]

Smoothest function which passes through given points?

Smoothness of harmonic functions

separately continuous functions $f: \mathbb{R}^2 \rightarrow \mathbb{R}$ but nowhere continuous

Interchanging Summation and Integral