Iteration semigroups with generalized convex, concave and affine elements.
A simultaneous system of functional inequalities and mappings which are weakly of a constant sign.
On principal iteration semigroups in the case of multiplier zero
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.
A pair of linear functional inequalities and a characterization of -norm
It is shown that, under some general algebraic conditions on fixed real numbers a,b,α,β, every solution f:ℝ → ℝ of the system of functional inequalities f(x+a) ≤ f(x)+α, f(x+b) ≤ f(x)+β that is continuous at some point must be a linear function (up to an additive constant). Analogous results for three other similar simultaneous systems are presented. An application to a characterization of -norm is given.
When is a -space?
Let be a Hausdorff locally convex space. Either or is a -space iff is of finite dimension (THEOREM). This is the most general solution of the problem studied by Iyahen [2] and Radenovič [3].
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