New posts in real-analysis

Prove that there exists $c\in[0,1]$ such that $\int_0^cf(t)dt=f(c)^3.$

real-analysis solution-verification

What is the function $f(x)$ which is differentiable everywhere and $f(x-1)f(x-2)+1=f(x)$?

real-analysis calculus functional-equations

Convexity and equality in Jensen's inequality

real-analysis convex-analysis

Convergence of a product series with one divergent factor

real-analysis sequences-and-series convergence-divergence

Outer measure of a union of 2 subsets of disjoint measurable sets of real numbers.

real-analysis measure-theory

Does Newton's method for inverting a series work?

calculus real-analysis sequences-and-series convergence-divergence

Computing $\sum_{n=1}^{\infty} \frac{\psi\left(\frac{n+1}{2}\right)}{ \binom{2n}{n}}$

calculus real-analysis integration definite-integrals

Show that if $A\subseteq B$, then inf $B\leq$ inf $A\leq$ sup $A \leq$ sup $B$

real-analysis inequality supremum-and-infimum

Evaluation of the double integral $\int_{[0,1]×[0,1]} \max\{x, y\} dxdy$

Do uniformly continuous functions map complete sets to complete sets?

real-analysis cauchy-sequences

Find all functions $f:\mathbb{R}^+\to \mathbb{R}^+$ such that for all $x,y\in\mathbb{R}^+$, $f(x)f(yf(x))=f(x+y)$

real-analysis analysis functions contest-math functional-equations

How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

real-analysis calculus integration definite-integrals catalans-constant

Is expectation Riemann-/Lebesgue–Stieltjes integral?

real-analysis integration probability-theory measure-theory functional-analysis

$f:[0,1]\to[0,1]$ be a continuous function. Let $x_1\in[0,1]$ and define $x_{n+1}={\sum_{i=1}^n f(x_i)\over n}$.Prove, $\{x_n\}$ is convergent

real-analysis sequences-and-series convergence-divergence continuity

Lebesgue Integral but not a Riemann integral

real-analysis measure-theory lebesgue-integral

Prove that if $f: \mathbb{R} \to \mathbb{Q}$ is continuous then $f$ is constant

real-analysis continuity

Is the series $\sum \sin^n(n)$ divergent?

Proving that, $|f'(x)-f'(y)|\le k|x-y| \implies (f'(x))^2< 2 kf(x) $

calculus real-analysis analysis functions lipschitz-functions

Hausdorff dimension of Cantor set

Differentiability implies Lipschitz continuity

real-analysis functional-analysis