ASYMPTOTIC BEHAVIOR OF $(a,k)$-REGULARIZED RESOLVENT FAMILIES AT ZERO

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.