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Browsing by Subject "continuous solutions"

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  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Asymptotic properties of solutions of some interative functional inequalities
    (2008) Brydak, Dobiesław; Choczewski, Bogdan; Czerni, Marek
    Continuous solutions of iterative linear inequalities of the first and second order are considered, belonging to a class $\mathcal{F}_T$ of functions behaving at the origin as a prescribed function $T$.
  • thumbnail.journal.alt
    Item type:Article, Access status: Open Access ,
    Continuous solutions of iterative equations of infinite order
    (2009) Kapica, Rafał; Morawiec, Janusz
    Given a probability space $(\Omega,\mathcal{A}, P)$ and a complete separable metric space $X$, we consider continuous and bounded solutions $\varphi: X \to \mathbb{R}$ of the equations $\varphi(x) = \int_{\Omega} \varphi(f(x,\omega))P(d\omega)$ and $\varphi(x) = 1-\int_{\Omega} \varphi(f(x,\omega))P(d\omega)$, assuming that the given function $f:X \times \Omega \to X$ is controlled by a random variable $L: \Omega \to (0,\infty)$ with $-\infty \lt \int_{\Omega} \log L(\omega)P(d\omega) \lt 0$. An application to a refinement type equation is also presented.