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A pair of linear functional inequalities and a characterization of $L^{p}$-norm

100%

Krassowska D., Matkowski J.

Annales Polonici Mathematici

2005

tom 85

nr 1

1-11

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 $L^{p}$-norm is given.

On principal iteration semigroups in the case of multiplier zero

100%

Krassowska D., Zdun M.

Open Mathematics

2013

tom 11

nr 1

177-187

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.

Ograniczanie wyników

1 Annales Polonici Mathematici

1 Open Mathematics

2 Krassowska D.

1 Matkowski J.

1 Zdun M.

1 2013

1 2005

Wyniki wyszukiwania

A pair of linear functional inequalities and a characterization of $L^{p}$-norm

On principal iteration semigroups in the case of multiplier zero