Functional Equation fx pfx − 1 − qfx − 2 and Its Hyers-Ulam Stability
2.Moreover,asubstantialpartofproofofTheorem 2.1canbederivedfromtheoremspresentedinthebooks 19,20 .However,the theorems in 19, 20 deal with solutions of the linear equation under some regularityconditions, for example, the continuity, convexity, diﬀerentiability, analyticity and so on,while Theorem 2.1 deals with the general solution of 1.7 without regularity conditions.
Note on nonstability of the linear functional equation of higher order
We provide a complete solution of the problem of Hyers-Ulam stability for a large class of higher order linear functional equations in single variable, with constant coefficients. We obtain this by showing that such an equation is nonstable in the case where at least one of the roots of the characteristic equation is of module 1. Our results are related to the notions of shadowing (in dynamical systems and computer science) and controlled chaos. They also correspond to some earlier results on approximate solutions of functional equations in single variable.
Struggles for Visibility
This article addresses the ways in which terrorists are rendered visible in the news media. By studying images used in coverage of terrorists, the article focuses on the visual construction of this figure, which symbolizes the public’s notion of the “enemy”, in terms of specific attacks and the general threat thereof as well as terrorist actors, networks, and ideologies. The article takes its point of departure in the assumption that two visual forms are prevalent for representing terrorists in the news media, “surveillance representations” and “self-representations”. Based on this assumption, the article is guided by a principal research question, namely: How are terrorists made visible in the news media through surveillance representations and self-representations and what are the prevalent genres for visually representing terrorist actors? The article draws on a theoretical framework concerning the news media’s propensity to personalize the terrorist and the mediated visibility of terrorists. Empirically, the article is based on a quantitative content analysis of coverage of terrorism by Danish public service broadcasters DR and TV2 in 2016 to provide an overview of the proportions between surveillance representations and self-representations and develop a typology of the most widespread genres: ID photography, surveillance footage, selfies and similar, and private snapshots.