In this paper, we intend to introduce the concept of c-K-gframes, which are the generalization of K-g-frames. In addition, we prove some new results on c-K-g-frames in Hilbert spaces. Moreover, we define the related operators of c-K-g frames. Then, we give necessary and sufficient conditions on c-K-g-frames to characterize them. Finally, we verify perturbation of c-K-g-frames.2010 Mathematics Subject Classification. Primary 42C15, 42C40.

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