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Assuming that the initial data are Hölder continuous on and transforming the original problem into homogeneous one, we prove that the state function is Hölder continuous on, for each.
Since is continuous on, for, where and.
Consider the time-varying discrete-time dynamical system (2.10) where is continuous on for all and is continuous on for all.
Let us denote by the set of functions which are absolutely continuous on for arbitrary small.
., with ( being the identity operator on X), for, the map is continuous on for every.
Since is uniformly continuous on, for any, there exist such that implies (2.27).
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com