Displaying similar documents to “Polynomials in the Volterra and Ritt operators”

The existence of solutions to a Volterra integral equation

Wojciech Mydlarczyk (1996)

Annales Polonici Mathematici

Similarity:

We study the equation u = k∗g(u) with k such that ln k is convex or concave and g is monotonic. Some necessary and sufficient conditions for the existence of nontrivial continuous solutions u of this equation are given.

New conditions for the existence of non trivial solutions to some Volterra equations.

W. Okrasinski (1990)

Extracta Mathematicae

Similarity:

We consider the following Volterra equation: (1)       u(x) = ∫0 x k(x-s) g(u(s)) ds,   where, k: [0, δ0] → R is an increasing absolutely continuous function such that k(0) = 0 g: [0,+ ∞) → [0,+ ∞) is an increasing absolutely continuous function such that g(0) = 0 and g(u)/u → ∞ as u → 0+ (see [3]). Let us note that (1) has always...

Rota-Baxter operators and Bernoulli polynomials

Vsevolod Gubarev (2021)

Communications in Mathematics

Similarity:

We develop the connection between Rota-Baxter operators arisen from algebra and mathematical physics and Bernoulli polynomials. We state that a trivial property of Rota-Baxter operators implies the symmetry of the power sum polynomials and Bernoulli polynomials. We show how Rota-Baxter operators equalities rewritten in terms of Bernoulli polynomials generate identities for the latter.