In a note at the end of his paper Recherches sur les fractions continues, Stieltjes gave a necessary and sufficient condition when a continued fraction is represented by a meromorphic function. This result is related to the study of compact Jacobi matrices. We indicate how this notion was developped and used since Stieltjes, with special attention to the results by M.G. Krein. We also pay atten...

In this paper, we improve some recent coupled fixed point resultsfor single-valued operators in the framework of ordered $b$-metricspaces established by Bota et al. [M-F. Bota, A. Petrusel, G.Petrusel and B. Samet, Coupled fixed point theorems forsingle-valued operators in b-metric spaces, Fixed Point TheoryAppl. (2015) 2015:231]. Also, we prove that Perov-type fix...

The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...

This note is devoted to the study of the dependence on p of the constant in the reverse Brunn-Minkowski inequality for p-convex balls (i.e. p-convex symmetric bodies). We will show that this constant is estimated as c ≤ C(p) ≤ C , for absolute constants c > 1 and C > 1. Let K ⊂ IR n and 0 < p ≤ 1. K is called a p-convex set if for any λ, μ ∈ (0, 1) such that λ + μ = 1 and for any points x, y ∈ ...

The covariance operator of a signal-plus-noise 0bserva:ion for a 2-parameter random field is factorized as products of Volterra type operators. As a result of this factorization we can express the determinant of this operator in terms of the system parameters. This determinant appears in the likelihood ratio that plays a significant role in identification and detection problems. Index Terms -Ra...

in this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the bag and samanta’s operator norm on felbin’s-type fuzzy normed spaces. in particular, the completeness of this space is studied. by some counterexamples, it is shown that the inverse mapping theorem and the banach-steinhaus’s theorem, are not valid for this fuzzy setting. also...

We investigate the strength of set existence axioms needed for separable Banach space theory. We show that a very strong axiom, Π1 comprehension, is needed to prove such basic facts as the existence of the weak-∗ closure of any norm-closed subspace of `1 = c0. This is in contrast to earlier work [6, 4, 7, 23, 22] in which theorems of separable Banach space theory were proved in very weak subsys...

In this paper, an attempt is made to present an extension of Darbo's theorem, and its applicationto study the solvability of a functional integral equation of Volterra type.