In this paper we introduce and study the new properties $(W {scriptstyle Pi})$, $(UW {scriptstyle Pi_a})$, $(UW {scriptstyle E})$ and $(UW {scriptstyle Pi}).$ The main goal of this paper is to study relationship between these new properties and other Weyl type theorems. Moreover, we reconsider several earlier results obtained respectively in cite{BK}, cite{RA2}, cite{DH}, cite{AB} and cite{BZ1} for which we give stronger versions.
展开▼