20.500.12556/RUL-120200 Stabilnost aditivnih preslikav in izometrij delo diplomskega seminarja Stability of additive transformations and isometries V diplomskem delu obravnavamo problem stabilnosti aditivnih preslikav in izometrij, oboje na evklidskih prostorih. Določimo vse zvezne preslikave, ki zadostijo Cauchyevi funkcijski enačbi na nekem evklidskem prostoru. Definiramo pojem $\delta$-aditivna preslikava za $\delta > 0$ in dokažemo, da za vsako $\delta$-aditivno preslikavo obstaja enolično določena aditivna preslikava, ki jo aproksimira. Pri tem je norma razlike manjša ali enaka $\delta$. Dokažemo tudi, da je $\delta$-aditivne preslikave $k$-tega reda za $k \ge 2$ mogoče aproksimirati z aditivnimi preslikavami. Pri tem se optimalna ocena aproksimacije izboljša. Dokažemo nekatere lastnosti izometrij in definiramo $\delta$-izometrijo za $\delta > 0$. Dokažemo, da za vsako $\delta$-izometrijo obstaja izometrija, za katero je norma razlike manjša od $10\delta$. The thesis addresses the problem of stability of additive transformations and isometries on euclidian spaces. Cauchy's functional equation is solved in the class of continious transformations. We define $\delta$-additive transformations for $\delta > 0$ and prove, that for every $\delta$-additive transformation there exists exactly one additive transformation, which approximates the former with norm of difference being less or equal to $\delta$. If we are dealing with $\delta$-additive transformation of $k$-th order for $k \ge 2$ the same property holds with a better approximation constant. We prove some properties of isometries and define $\delta$-isometries for $\delta > 0$. We prove that every $\delta$-isometry can be approximated by an isometry with the norm of difference being less than $10\delta$. stabilnost funkcijskih enačb aditivne preslikave izometrije stability of functional equations additive transformations isometries true false false Slovenski jezik Angleški jezik Delo diplomskega seminarja/zaključno seminarsko delo/naloga 2020-09-17 08:15:45 2020-09-17 08:15:48 2024-05-29 14:34:11 0000-00-00 00:00:00 2020 0 0 0000-00-00 NiDoloceno NiDoloceno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 517.5 110553 58714371 1480.pdf 1480.pdf 1 6527F42CA83497E3F2A68851AAD548AA 2fc973f3e95be234b489735efc818d12989ff6c1517c3eb9b2e7145e44d445b7 064ab052-a1ba-11eb-a523-00155dcfd717 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=134978 Fakulteta za matematiko in fiziko 0 0 0