Strong Convergence of Generalized Resolvents

Lina Aryati(1*)

(*) Corresponding Author


Let M and fLng be a linear, closed, densely defined operator and a sequence of linear, closed, densely defined operators in a Banach Space X respectively. We consider a sequence of generalized resolvents fRn(¸)g, where Rn(¸) = (Ln¡¸M)¡1M. In this paper, we will prove that the sequence fRn(¸)g is uniformly bounded in n and ¸ in any compact subset of a certain open set. Then we will concern with consideration on strong convergence of fRn(¸)g. Finally we will give a criterion for the sequence fRn(¸)g converges strongly.

Keywords : generalized resolvent, uniformly bounded, strong convergence

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ISSN 0215-9309 (Print)

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