University of MaraghehSahand Communications in Mathematical Analysis2322-580701220141201On X ̃-frames and conjugate systems in Banach spaces192911273ENMigdadIsmailovDepartment of Non-harmonic analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.AfetJabrailovaDepartment of Functional analysis, Institute of Mathematics and Mechanics of NAS of Azerbaijan, Baku, Azerbaijan.Journal Article20140425The generalization of p-frame in Banach spaces is considered in this paper. The concepts of an $tilde{X}$-frame and a system conjugate to $tilde{X}$-frame were introduced. Analogues of the results on the existence of conjugate system were obtained. The stability of $tilde{X}$-frame having a conjugate system is studied.http://scma.maragheh.ac.ir/article_11273_0356133177a286fc7ca41146dd50c9bf.pdf