On a measure of noncompactness in the space of regulated functions and its applications
In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Amon...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2018-06-01
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| Series: | Advances in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/anona-2018-0024 |
| Summary: | In this paper we formulate a criterion for relative compactness in the space of functions regulated on a bounded and closed interval. We prove that the mentioned criterion is equivalent to a known criterion obtained earlier by D. Fraňkova, but it turns out to be very convenient in applications. Among others, it creates the basis to construct a regular measure of noncompactness in the space of regulated functions. We show the applicability of the constructed measure of noncompactness in proving the existence of solutions of a quadratic Hammerstein integral equation in the space of regulated functions. |
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| ISSN: | 2191-9496 2191-950X |