Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations
The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-12-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/12/2205 |
| _version_ | 1797379312759865344 |
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| author | Cemil Tunç Fehaid Salem Alshammari Fahir Talay Akyildiz |
| author_facet | Cemil Tunç Fehaid Salem Alshammari Fahir Talay Akyildiz |
| author_sort | Cemil Tunç |
| collection | DOAJ |
| description | The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric. |
| first_indexed | 2024-03-08T20:20:20Z |
| format | Article |
| id | doaj.art-ba726bb04c6946bfb7cd7d6164f7ba18 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-08T20:20:20Z |
| publishDate | 2023-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-ba726bb04c6946bfb7cd7d6164f7ba182023-12-22T14:45:24ZengMDPI AGSymmetry2073-89942023-12-011512220510.3390/sym15122205Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral EquationsCemil Tunç0Fehaid Salem Alshammari1Fahir Talay Akyildiz2Department of Mathematics, Faculty of Sciences, Van Yuzuncu Yil University, Van 65090, TurkeyDepartment of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi ArabiaDepartment of Mathematics and Statistics, Faculty of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi ArabiaThe authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.https://www.mdpi.com/2073-8994/15/12/2205existence and uniqueness of solutionsnonlinear HTFIEfixed pointprogressivecontractionChebyshev norm |
| spellingShingle | Cemil Tunç Fehaid Salem Alshammari Fahir Talay Akyildiz Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations Symmetry existence and uniqueness of solutions nonlinear HTFIE fixed point progressive contraction Chebyshev norm |
| title | Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations |
| title_full | Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations |
| title_fullStr | Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations |
| title_full_unstemmed | Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations |
| title_short | Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations |
| title_sort | existence and uniqueness of solutions of hammerstein type functional integral equations |
| topic | existence and uniqueness of solutions nonlinear HTFIE fixed point progressive contraction Chebyshev norm |
| url | https://www.mdpi.com/2073-8994/15/12/2205 |
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