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

100%

Olszowy L.

Commentationes Mathematicae

2008

tom Vol. 48, [Z] 1

103-112

We show that [formula] is a measure of noncompactness defined on some subsets of the space C(R+) = {x : R+ !R, x 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.

Measures of noncompactness related to monotonicity

63%

Banaś J. , Olszowy L.

tom [Z] 41

13-23

We investigate measures of noncompactness related to the monotonicity of functions. Several properties of these measures of non-compactness are derived. Particularly we give the estimates of these measures with help of the Hausdorff distance from the family of nondecreasing or nonincreasing functions. Such a result indicates some connections with approximation theory.

The superposition operator for vector-valued functions on a noncompact interval

63%

Dronka J. , Olszowy L.

2006

tom Vol. 39, nr 2

411-418

In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a noncompact interval is considered. Acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation in this space is obtained.