Abstract
This paper is concerned with the ergodicity and strong stability for (b, l)-regularized resolvent operator families. First, we study Abel ergodicity and Cesaro ergodicity of (b, l)-regularized resolvent operator families by using the methods of operator theory and complex Tauberian theorem. And then, by constructing a new operator-valued function, we obtain some sufficient conditions on the strong stability of bounded (b, l)-regularized resolvent operator families by means of Cauchy theorem and Riemann–Lebesgue lemma. Our results generalize the related conclusions for operator semigroups and resolvent operator families.
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