University of MaraghehSahand Communications in Mathematical Analysis2322-580717320200701Continuous $ k $-Frames and their Dual in Hilbert Spaces1451604058310.22130/scma.2019.115719.691ENGholamrezaRahimlouDepartment of Mathematics, Shabestar Branch,Islamic Azad University, Shabestar, Iran.RezaAhmadiInstitute of Fundamental Science, University of Tabriz, Tabriz, Iran.Mohammad AliJafarizadehFaculty of Physic, University of Tabriz, Tabriz, Iran.SusanNamiFaculty of Physic, University of Tabriz, Tabriz, Iran.Journal Article20191014The notion of $k$-frames was recently introduced by G\u avru\c ta in HilbertĀ spaces to study atomic systems with respect to a bounded linear operator. A continuous frame is a family of vectors in a Hilbert space which allows reproductions of arbitrary elements by continuous super positions. In this manuscript, we construct a continuous $k$-frame, so called c$k$-frame along with an atomic system for this version of frames. Also we introduce a new method for obtaining the dual of a c$k$-frame and prove some new results about it.https://scma.maragheh.ac.ir/article_40583_dc1f525dd6b30726e40f65c66c109e27.pdf