4 problems

Khabibullin's conjecture. The stated integral implication holds for every such $S$, every $\rho>1$, and every integer $n\geq 2$. This is an extremal integral inequality arising in…

Let $\lambda$ be a positive real number and let $n$ be an integer with $n\geqslant 2$. Let $S(x)$ be a nonnegative nondecreasing function on $[0,+\infty)$. If … for every…

Let $n<1$, let $ugeq 1-n+\sqrt{2(1-n)}$, and define … For the modified Bessel function of the second kind $K_\mu$, the author conjectures that, for every $x>0$, … The exponent shif…

Let $[? Let$[?