• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.439-452
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• 2015

In this paper we introduce and study the new properties ($W_{\Pi}$), ($UW_{{\Pi}_a}$), ($UW_E$) and ($UW_{\Pi}$). 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 [11], [18], [14], [1] and [13] for which we give stronger versions.