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Solving some functional and operational equations.

Olteanu, Alina, Olteanu, Octav (2008)

APPS. Applied Sciences

Some complex matrix and determinant functional equations.

Risteski, I.B., Covachev, V.C. (2006)

Acta Mathematica Universitatis Comenianae. New Series

Some propositions related to a dilation theorem of W. Benz.

John AQ. Baker (1994)

Aequationes mathematicae

Submultiplicative functions and operator inequalities

Hermann König, Vitali Milman (2014)

Studia Mathematica

Let T: C¹(ℝ) → C(ℝ) be an operator satisfying the “chain rule inequality” T(f∘g) ≤ (Tf)∘g⋅Tg, f,g ∈ C¹(ℝ). Imposing a weak continuity and a non-degeneracy condition on T, we determine the form of all maps T satisfying this inequality together with T(-Id)(0) < 0. They have the form Tf = ⎧ $(H \circ f / H) f^{' p}$ , f’ ≥ 0, ⎨ ⎩ $- A (H \circ f / H) | f^{'} |^{p}$ , f’ < 0, with p > 0, H ∈ C(ℝ), A ≥ 1. For A = 1, these are just the solutions of the chain rule operator equation. To prove this, we characterize the submultiplicative, measurable functions...

Sur les opérations en général et les équations différentielles linéaires d'ordre infini

C. Bourlet (1897)

Annales scientifiques de l'École Normale Supérieure

Sur les transmutations