This paper is concerned with the insight that the wavelet-type K-frame is the promotion of the wavelet-type frame,and the discussion of the properties and stability of the frame is conducive to the study of frames with special structural forms in Hilbert space.The study works by defining the wavelet K-frame combining the concepts of K-frames and wavelet-type frames;obtaining a necessary and sufficient condition for wavelet-type compact K-frames to be wavelet-type frames by studing the relationship between wavelet-type K-frames and wavelet-type frames,and giving a general perturbation theorem of K-frames,by which analyzing the definition of the stability of wavelet-type K-frames.The gained results generalize the existing conclusion on the perturbation properties of wavelet frames and K-frames in Hilbert spaces.
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