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

Leszek Olszowy. "On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval." Commentationes Mathematicae 48.1 (2008): null. <http://eudml.org/doc/291717>.

@article{LeszekOlszowy2008,
abstract = {We show that $\omega _0 (X) = \lim _\{T\rightarrow \infty \} \lim _\{\varepsilon \rightarrow 0\} \omega ^T (X, \varepsilon )$ is a measure of noncompactness defined on some subsets of the space $C(\mathbb \{R\}^+) = \lbrace x\colon \mathbb \{R\}^+ \rightarrow \mathbb \{R\},\ x\ \text\{continuous\}\rbrace $ 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.},
author = {Leszek Olszowy},
journal = {Commentationes Mathematicae},
keywords = {Quadratic Urysohn integral; measure of noncompactness; Tichonov fixed point theorem},
language = {eng},
number = {1},
pages = {null},
title = {On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval},
url = {http://eudml.org/doc/291717},
volume = {48},
year = {2008},
}

TY - JOUR
AU - Leszek Olszowy
TI - On existence of solutions of a quadratic Urysohn integral equation on an unbounded interval
JO - Commentationes Mathematicae
PY - 2008
VL - 48
IS - 1
SP - null
AB - We show that $\omega _0 (X) = \lim _{T\rightarrow \infty } \lim _{\varepsilon \rightarrow 0} \omega ^T (X, \varepsilon )$ is a measure of noncompactness defined on some subsets of the space $C(\mathbb {R}^+) = \lbrace x\colon \mathbb {R}^+ \rightarrow \mathbb {R},\ x\ \text{continuous}\rbrace $ 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.
LA - eng
KW - Quadratic Urysohn integral; measure of noncompactness; Tichonov fixed point theorem
UR - http://eudml.org/doc/291717
ER -