In this paper, we investigated the concept of ε-diskcyclic operators on a separable infinite-dimensional Hilbert space . A bounded linear operator  is called -diskcyclic if there exists a vector in  such that its disk orbit  visits every cone of aperture . That is, for every non-zero vector in , there exist in  where  and  in  such that . Such a vector  is then called an ε-diskcyclic vector for .

We established several properties of ε-diskcyclic operators. In particular, we showed that every -diskcyclic operator is cyclic. Moreover, we examined the relationship between ε-diskcyclic vectors of  and eigenvectors of the adjoint operator  that cannot be orthogonal to each other. We also proved that if  is a bounded linear operator on ; , then the direct sum  ​ is -diskcyclic provided each  is -diskcyclic. Finally, we presented a criterion for determining -diskcyclicity