%0 Journal Article %T Generalized Continuous Frames for Operators %J Sahand Communications in Mathematical Analysis %I University of Maragheh %Z 2322-5807 %A .Shekhar, Chander %A Bhati, Sunayana %A Rathore, G.S. %D 2020 %\ 06/01/2020 %V 17 %N 2 %P 185-201 %! Generalized Continuous Frames for Operators %K Frames %K K-frames %K Continuous frames %R 10.22130/scma.2018.97329.523 %X 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. %U https://scma.maragheh.ac.ir/article_37409_fa26e1468b04482563c581f767572d35.pdf