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A bounded linear operator T on a complex Hilbert space H is called(n, k)-quasi-*-paranormal if ║T~(1+n)(T~kx) ║~(1/(1+n))║ T~kx║~(n/(1+n))≥║ T*(T~kx)║ for all x ∈ H,where n, k are nonnegative integers. This class of operators has many interesting properti