In this note, we aim to show that several known generalizations of frames are equivalent to the Continuous frame defined by Ali et al. in 1993. Indeed, it is shown that these generalizations can be considered as an operator between two Hilbert spaces.

In this note, the notion of generalized Continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized Continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized Continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized Continuous $K$-frame for $ \mathcal{H} $ with respect to $ \mu $ is given. Also, a sufficient condition for a generalized Continuous $K$-frame is given.  Further, among other results, we prove that generalized Continuous $K$-frames are invariant under a linear  homeomorphism. Finally, keeping in mind the importance of perturbation theory in various branches of applied mathematics, we study perturbation of $K$-frames and obtain conditions for the stability of generalized Continuous $K$-frames.

K-g-frames, as an extension of g-frames and K-frames are one of the active fields in frame theory. In this paper, we consider Continuous K-g-frames which are a generalization of discrete K-g-frames. We give the necessary and sufficient conditions to characterize their duals. For example, the canonical dual of a given K-g-frame is described by both its frame operator and its alternate duals.

In this paper, we study the concept of multipliers for the Continuous $g$-Bessel families in Hilbert spaces. We present necessary conditions for invertibility of multipliers for the Continuous $g$-Bessel families and sufficient conditions for invertibility of multipliers for Continuous $g$-frames.

The study of the c$k$-fusions frames shows that the emphasis on the measure spaces introduces a new idea, although some similar properties with the discrete case are raised. Moreover, due to the nature of measure spaces, we have to use new techniques for new results. Especially, the topic of the dual of frames  which is important for frame applications, have been specified  completely for the Continuous frames. After improving and extending the concept of fusion frames and Continuous frames, in this paper we introduce Continuous $k$-fusion frames in Hilbert spaces. Similarly to the c-fusion frames, dual of Continuous $k$-fusion frames may not be defined, we however define the $Q$-dual of Continuous $k$-fusion frames. Also some new results and the perturbation of Continuous $k$-fusion frames will be presented.

In the present paper, we study Continuous frames in Hilbert $C^*$-modules and present some results of these frames. Next, we give the concept of dual Continuous frames in Hilbert $C^*$-modules and investigate some properties of them. Also, by introducing the notion of the similarity of the Continuous frames, characterizing it, and stating some of its properties, we refer to the investigation of the effect of similarity on the dual Continuous frames in Hilbert $C^*$-modules.

Let $\mathcal{U}$ be a Hilbert $\mathcal{A}$-module and $L(\mathcal{U})$ be the set of all adjointable $\mathcal{A}$-linear maps on $\mathcal{U}$. Let $K$ and $L$ be two Continuous $g$-frames for $\mathcal{U}$. Then $K$ is similar with $L$ if there exists an invertible operator $J\in L(\mathcal{U})$ such that $JK =L$. In this paper, we show that if $K$ and $L$ are near, then they are similar via some invertible operator $J$. Recall that two Continuous $g$-frames $K$ and $L$ are near if $K$ is close to $L$ and $L$ is close to $K$. We also describe closeness bound between two Continuous $g$-frames for $\mathcal{U}$.