In this paper, we offer a new stability concept, practical Ulam-Hyers-Rassias stability, for nonlinear equations in Banach spaces, which consists in a restriction of Ulam-Hyers-Rassias stability to bounded subsets. We derive some interesting sufficient conditions on practical Ulam-Hyers-Rassias stability from a nonlinear functional analysis point of view. Our method is based on solving nonlinear equations via homotopy method together with Bihari inequality result. Then we consider nonlinear equations with surjective asymptotics at infinity. Moore-Penrose inverses are used for equations defined on Hilbert spaces. Specific practical Ulam-Hyers-Rassias results are derived for finite-dimensional equations. Finally, two examples illustrate our theoretical results.
Proboštství Baštiny založil ostrovský klášter v předhusitském období v odlehlé části souvislého brdského lesa. Studie, jež vychází z povrchového průzkumu zaniklé lokality v r. 2008, zkoumá vnitřní uspořádání a zázemí tohoto svébytného monastického areálu a porovnává výsledky se stavem poznání závislých mnišských domů malého rozsahu v západní Evropě. and The Baštiny Priory was founded by the Ostrov monastery in the pre-Hussite period in an outlying part of an extended forest in the Central Bohemian Uplands of Brdy. This study, which is based on a surface survey, examines the internal arrangement and the background of this unique monastic site and compares the results with the state of knowledge of small monastic houses in other parts of Europe.
This article describes parallels between Roman procedural law and trends incorporating sociology in legal science. The author is persuaded that legal theoreticians at the end of the nineteenth century must have been inspired by Roman law, and in particular by praetorian law. The leader of these lawyers was a Romanist Eugen Ehrlich, so-called “the founder of legal sociology”. The author gives detailed attention to the dichotomy between the free and bounded approach in the application of law, specifically with regard to the
filling-in of gaps in the law. In the conclusion the author proposes that we be inspired by Ehrlich’s theory, especially by the fight against contra-factual norms of state law, which are of course in conflict with social law.