"functional analysis linear nonlinear Lipschitz Banach space differential equation"@en . "N\u00E1vrh se zab\u00FDv\u00E1 abstraktn\u00EDmi probl\u00E9my z oblasti neline\u00E1rn\u00EDch zobrazen\u00ED mezi Banachov\u00FDmi prostory a jejich podmno\u017Einami. Pro snaz\u0161\u00ED orientaci je vhodn\u00E9 projekt rozd\u011Blit do n\u00E1sleduj\u00EDc\u00EDch\u00A0p\u011Bti vz\u00E1jemn\u011B souvisej\u00EDc\u00EDch podoblast\u00ED:1. Obecn\u00E9 vlastnosti uniformn\u00EDch zobrazen\u00ED, jejich redukce na lischitzovsk\u00E1 zobrazen\u00ED a jejich topologick\u00E9 a metrick\u00E9 vlastnosti.2. Linearizace lipschitzovsk\u00FDch zobrazen\u00ED, existence derivace. 3. Struktura z\u00FA\u010Dastn\u011Bn\u00FDch prostor\u016F, v\u00FDsledky z line\u00E1rn\u00ED teorie. 4. Souvislost s renormacemi Banachov\u00FDch prostor\u016F. 5. \u00A0Aplikace v jin\u00FDch oblastech matematiky, obzvl\u00E1\u0161t\u011B v teorii pevn\u00FDch bod\u016F zobrazen\u00ED a v\u00A0diferenci\u00E1ln\u00EDch rovnic\u00EDch. P\u0159\u00EDklady konkr\u00E9tn\u00EDch probl\u00E9m\u016F. Jsou klasick\u00E9 Banachovy prostory funkc\u00ED isomorfn\u00ED sv\u00FDm uniformn\u011B homeomorfn\u00EDm obraz\u016Fm? Je jednotkov\u00E1 koule v\u017Edy uniformn\u011B homeomorfn\u00ED jednotkov\u00E9 sf\u00E9\u0159e? Jak\u00E9 jsou komplementovan\u00E9 podprostory\u00A0klasick\u00FDch prostor\u016F funkc\u00ED? Maj\u00ED reflexivn\u00ED Banachovy prostory vlastnost pevn\u00FDch bod\u016F pro neexpanz\u00EDvn\u00ED zobrazen\u00ED?" . . "2011-01-01+01:00"^^ . . . "1"^^ . "2014-04-18+02:00"^^ . "Nonlinear functional analysis"@en . . . "2"^^ . . . . "0"^^ . . . . . . "2015-12-31+01:00"^^ . . . "http://www.isvav.cz/projectDetail.do?rowId=GAP201/11/0345"^^ . "16"^^ . . . "16"^^ . "GAP201/11/0345" . "The subject of our proposal are abstract problems concerning nonlinear mappings between Banach spaces and their subsets. For easier orientation, it is convenient to divide the project into the following five interdependent areas. 1. General properties of uniform mappings, their reduction to Lipschitz mappings, and their metric properties. 2. Linearization properties of Lipschitz mappings, in particular the existence of derivatives. 3. Structural properties of participating spaces, linear theory. 4. Renormings of Banach spaces. 5. Applications to other areas of mathematics, such as fixed point theory and differential equations. Concrete examples of the proposed problems. Are the classical Banach function\u00A0spaces linearly isomorphic to their uniformly homeomorphic images? Is the unit ball uniformly homeomorphic to the unit sphere? Are Lipschitz isomorphic separable Banach spaces linearly isomorphic? What are the complemented subspaces of the classical function Banach spaces? Do reflexive Banach spaces have a fixed point property for nonexpansive mappings?"@en . "2015-04-23+02:00"^^ . "Neline\u00E1rn\u00ED funkcion\u00E1ln\u00ED anal\u00FDza" .