Abstract: This paper gives sufficient conditions for the existence of positive periodic solutions to general indefinite singular differential equations. Furthermore, under some assumptions we show the existence of two positive periodic solutions. The methods used are Krasnoselski\(\breve{\mbox{i}}\)’s-Guo fixed point theorem and the positivity of the associated Green’s function.

Abstract: Fusion frames and subfusion frames are generalizations of frames in the Hilbert spaces. In this paper, we study subfusion frames and the relations between the fusion frames and subfusion frame operators. Also, we introduce new construction of subfusion frames. In particular, we study atomic resolution of the identity on the Hilbert spaces and derive new results.

Abstract: In this work, a new class of bi-univalent functions \(I^{n+1}_{\Gamma_m,\lambda}(x,z)\) is defined by means of subordination. Upper bounds for some initial coefficients and the Fekete-Szegö functional of functions in the new class were obtained.