On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations
Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231562?viewType=HTML |
| _version_ | 1797450905203769344 |
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| author | Ateq Alsaadi Manochehr Kazemi Mohamed M. A. Metwali |
| author_facet | Ateq Alsaadi Manochehr Kazemi Mohamed M. A. Metwali |
| author_sort | Ateq Alsaadi |
| collection | DOAJ |
| description | Regarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces. |
| first_indexed | 2024-03-09T14:47:15Z |
| format | Article |
| id | doaj.art-39572b950f31482693ecf79fa18945d8 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-09T14:47:15Z |
| publishDate | 2023-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-39572b950f31482693ecf79fa18945d82023-11-27T01:31:00ZengAIMS PressAIMS Mathematics2473-69882023-11-01812305623057310.3934/math.20231562On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equationsAteq Alsaadi0Manochehr Kazemi 1Mohamed M. A. Metwali 21. Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia2. Department of Mathematics, Ashtian Branch, Islamic Azad University, Ashtian, Iran3. Department of Mathematics and Computer Science, Faculty of Science, Damanhour University, Damanhour, EgyptRegarding the Hausdorff measure of noncompactness, we provide and demonstrate a generalization of Petryshyn's fixed point theorem in Banach algebras. Comparing this theorem to Schauder and Darbo's fixed point theorems, we can skip demonstrating closed, convex and compactness properties of the investigated operators. We employ our fixed point theorem to provide the existence findings for the product of $ n $-nonlinear integral equations in the Banach algebra of continuous functions $ C(I_a) $, which is a generalization of various types of integral equations in the literature. Lastly, a few specific instances and informative examples are provided. Our findings can successfully be extended to several Banach algebras, including $ AC, C^1 $ or $ BV $-spaces.https://www.aimspress.com/article/doi/10.3934/math.20231562?viewType=HTMLpetryshyn's fixed point theorem (f.p.t.)measures of noncompactness (m.n.c.)product of $ n $-nonlinear integral equations |
| spellingShingle | Ateq Alsaadi Manochehr Kazemi Mohamed M. A. Metwali On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations AIMS Mathematics petryshyn's fixed point theorem (f.p.t.) measures of noncompactness (m.n.c.) product of $ n $-nonlinear integral equations |
| title | On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations |
| title_full | On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations |
| title_fullStr | On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations |
| title_full_unstemmed | On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations |
| title_short | On generalization of Petryshyn's fixed point theorem and its application to the product of n-nonlinear integral equations |
| title_sort | on generalization of petryshyn s fixed point theorem and its application to the product of n nonlinear integral equations |
| topic | petryshyn's fixed point theorem (f.p.t.) measures of noncompactness (m.n.c.) product of $ n $-nonlinear integral equations |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231562?viewType=HTML |
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