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National Repository of Grey Literature 3 records found  Search took 0.00 seconds. 
Semiconvex functions and its differences
 Kryštof, Václav ; Zajíček, Luděk (advisor) ; Johanis, Michal (referee)
The main result of this thesis is that we prove certain versions of Ilmanen's lemmma. That means - given semiconvex (or locally semiconvex) function f1 and semiconcave (or locally semiconcave) function f2 such that f1 ≤ f2 we find a function f such that f1 ≤ f ≤ f2 and f is both semiconvex and semiconcave (or locally uniformly differentiable). We also give characterization (via a new variation) of those functions which are the difference of two ω-nondecreasing functions 1
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Semiconvex functions and its differences
 Kryštof, Václav ; Zajíček, Luděk (advisor) ; Johanis, Michal (referee)
The main result of this thesis is that we prove certain versions of Ilmanen's lemmma. That means - given semiconvex (or locally semiconvex) function f1 and semiconcave (or locally semiconcave) function f2 such that f1 ≤ f2 we find a function f such that f1 ≤ f ≤ f2 and f is both semiconvex and semiconcave (or locally uniformly differentiable). We also give characterization (via a new variation) of those functions which are the difference of two ω-nondecreasing functions 1
Detailed record
Semiconvex functions and their differences
 Kryštof, Václav ; Zajíček, Luděk (advisor) ; Zelený, Miroslav (referee)
Semiconvex functions generalize convex functions on a normed linear space. In this thesis we deal with semiconvex functions of one real varia- ble, so with a special case. In the first part we especially study properties of semiconvex functions from one-side derivative point of view and give charac- terization of locally semiconvex functions on an open interval by right-hand derivative. The second part of the thesis concerns functions which are a dif- ference of two semiconvex functions. Also in this case we give (by right-hand derivative) characterization of functions which are a difference of two locally semiconvex functions on an open interval. This is related to a generalized va- riation which we introduce and which enables to characterize those functions which are a difference of two semiconvex functions on an open interval with modulus Mω, where M ∈ (0, ∞). 1
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