Concave iteration semigroups of linear set-valued functions

Jolanta Olko

Displaying similar documents to “Concave iteration semigroups of linear set-valued functions”

Concave iteration semigroups of linear continuous set-valued functions

Andrzej Smajdor, Wilhelmina Smajdor (2012)

Open Mathematics

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Let F t: t ≥ 0 be a concave iteration semigroup of linear continuous set-valued functions defined on a convex cone K with nonempty interior in a Banach space X with values in cc(K). If we assume that the Hukuhara differences F 0(x) − F t (x) exist for x ∈ K and t > 0, then D t F t (x) = (−1)F t ((−1)G(x)) for x ∈ K and t ≥ 0, where D t F t (x) denotes the derivative of F t (x) with respect to t and $G (x) = lim_{s \to 0} (F^{0} (x) - F^{s} (x)) / (- s)$ for x ∈ K.

On principal iteration semigroups in the case of multiplier zero

Dorota Krassowska, Marek Zdun (2013)

Open Mathematics

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We collect and generalize various known definitions of principal iteration semigroups in the case of multiplier zero and establish connections among them. The common characteristic property of each definition is conjugating of an iteration semigroup to different normal forms. The conjugating functions are expressed by suitable formulas and satisfy either Böttcher’s or Schröder’s functional equation.