Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators

In this paper we use the general class of contractive-like operators introduced by Bosede and Rhoades (J. Adv. Math. Stud. 3(2):1-3, 2010) to prove strong convergence and stability results for Picard-Mann hybrid iterative schemes considered in a real normed linear space. We establish the strong convergence and stability of the Picard iterative scheme as a corollary. Our results generalize and improve a multitude of results in the literature, including the recent results of Chidume (Fixed Point Theory Appl. 2014:233, 2014)

X-ray spectropolarimetric measurements of the Kerr metric

It is thought that the spacetime geometry around black hole candidates is described by the Kerr solution, but an observational confirmation is still missing. Today, the continuum-fitting method and the analysis of the iron K$\alpha$ line cannot unambiguously test the Kerr paradigm because of the degeneracy among the parameters of the system, in the sense that it is impossible with current X-ray data to distinguish a Kerr black hole from a non-Kerr object with different values of the model parameters. In this paper, we study the possibility of testing the Kerr nature of black hole candidates with X-ray spectropolarimetric measurements. Within our simplified model that does not include the effect of returning radiation, we find that it is impossible to test the Kerr metric and the problem is still the strong correlation between the spin and possible deviations from the Kerr geometry. Moreover, the correlation is very similar to that of other two techniques, which makes the combination of different measurements not very helpful. Nevertheless, our results cannot be taken as conclusive and, in order to arrive at a final answer, the effect of returning radiation should be properly taken into account.Comment: 12 pages, 8 figures. v2: refereed versio

Accreting Black Holes

This chapter provides a general overview of the theory and observations of black holes in the Universe and on their interpretation. We briefly review the black hole classes, accretion disk models, spectral state classification, the AGN classification, and the leading techniques for measuring black hole spins. We also introduce quasi-periodic oscillations, the shadow of black holes, and the observations and the theoretical models of jets.Comment: 41 pages, 18 figures. To appear in "Tutorial Guide to X-ray and Gamma-ray Astronomy: Data Reduction and Analysis" (Ed. C. Bambi, Springer Singapore, 2020). v3: fixed some typos and updated some parts. arXiv admin note: substantial text overlap with arXiv:1711.1025

New Insights into X-ray Binaries

X-ray binaries are excellent laboratories to study collapsed objects. On the one hand, transient X-ray binaries contain the best examples of stellar-mass black holes while persistent X-ray binaries mostly harbour accreting neutron stars. The determination of stellar masses in persistent X-ray binaries is usually hampered by the overwhelming luminosity of the X-ray heated accretion disc. However, the discovery of high-excitation emission lines from the irradiated companion star has opened new routes in the study of compact objects. This paper presents novel techniques which exploits these irradiated lines and summarises the dynamical masses obtained for the two populations of collapsed stars: neutron stars and black holes.Comment: 12 pages, 5 figures, 2 tables, Invited review to plenary session in "Highlights of Spanish Astrophysics V", Proceedings of the VIII Scientific Meeting of the Spanish Astronomical Society (SEA) held in Santander, 7-11 July, 2008. Edited by J. Gorgas, L. J. Goicoechea, J. I. Gonzalez-Serrano, J. M. Dieg