Measure of noncompactness and a generalized Darbo’s fixed point theorem and its applications to a system of integral equations
Abstract Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2020-05-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://link.springer.com/article/10.1186/s13662-020-02703-z |
| Summary: | Abstract Işık et al. (Mathematics 7:862, 2019) presented an interesting generalization of the Banach contraction principle. In this paper, motivated by Işık et al., we give a new extension of the well-known Darbo inequality in a Banach space. Our results provide several generalizations of the Darbo inequality. As an application, we study the existence of solutions for a system of functional integral equations in C [ 0 , T ] $C[0,T]$ . Finally, we expose a genuine example to support the effectiveness of our results. |
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| ISSN: | 1687-1847 |