Harmonic functions via restricted mean-value theorems

Mohammad Javaheri

Let $f$ be a function on a bounded domain $\Omega \subseteq {\mathbb{R}}^n$ and $\delta$ be a positive function on $\Omega$ such that $B(x,\delta (x))\subseteq \Omega$. Let $\sigma (f)(x)$ be the average of $f$ over…