On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval

• Autorzy: Leszek Olszowy
• Języki publikacji: EN

Abstrakty

EN

We show that \(\omega_0 (X) = \lim_{T\to\infty} \lim_{\varepsilon\to 0} \omega^T (X, \varepsilon)\) is a measure of noncompactness defined on some subsets of the space \(C(\mathbb{R}^+) = \{x\colon \mathbb{R}^+ \to \mathbb{R},\ x\ \text{continuous}\}\) furnished with the distance defined by the family of seminorms \(|x|_n\). Moreover, using a technique associated with the measures of noncompactness, we prove the existence of solutions of a quadratic Urysohn integral equation on an unbounded interval. This measure allows to obtain theorems on the existence of solutions of a integral equations on an unbounded interval under a weaker assumptions then the assumptions of theorems obtained by applying two-component measures of noncompactness.

Słowa kluczowe

EN

Quadratic Urysohn integral; measure of noncompactness; Tichonov fixed point theorem

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: 48
• Numer: 1

Daty

wydano

2008

online

2017-12-19

Twórcy

autor

Leszek Olszowy

Identyfikatory

DOI

10.14708/cm.v48i1.5264