Abstract
This paper is primarily concerned with approximation at 0 of an $(a,k)$-regularized resolvent family $R(\cdot)$ for Volterra integral equation. We shall consider convergence rates of some kind of local means $Q_m(t)$, $t \geq 0$, $m \geq 0$, of $R(t)/k(t)$. Some approximation theorems and local ergodic theorems with rates will be deduced from general approximation theorems for regularized approximation processes.
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