Infinite Geraghty type extensions and their applications on integral equations
Abstract In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019)....
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2021-10-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-021-03583-7 |
| _version_ | 1818890682919550976 |
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| author | R. Bardhan C. Ozel L. Guran H. Aydi Choonkil Park |
| author_facet | R. Bardhan C. Ozel L. Guran H. Aydi Choonkil Park |
| author_sort | R. Bardhan |
| collection | DOAJ |
| description | Abstract In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). We also prove a similar Geraghty type construction for Fisher (Math. Mag. 48(4):223–225, 1975) in an infinite dimension using similar techniques as in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018) and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). As an application, we ensure the existence of solutions for infinite dimensional Fredholm integral equation and Uryshon type integral equation. |
| first_indexed | 2024-12-19T17:28:48Z |
| format | Article |
| id | doaj.art-5925229334814c4d9f14102a70a953a5 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-19T17:28:48Z |
| publishDate | 2021-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-5925229334814c4d9f14102a70a953a52022-12-21T20:12:30ZengSpringerOpenAdvances in Difference Equations1687-18472021-10-012021111910.1186/s13662-021-03583-7Infinite Geraghty type extensions and their applications on integral equationsR. Bardhan0C. Ozel1L. Guran2H. Aydi3Choonkil Park4Tezpur UniversityDepartment of Mathematics, Faculty of Sciences, King Abdulaziz UniversityDepartment of Pharmaceutical Sciences, “Vasile Goldiş” Western University of AradInstitut Supérieur d’Informatique et des Techniques de Communication, Université de SousseResearch Institute for Natural Sciences, Hanyang UniversityAbstract In this article, we discuss about a series of infinite dimensional extensions of some theorems given in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018), (Fisher in Math. Mag. 48(4):223–225, 1975), and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). We also prove a similar Geraghty type construction for Fisher (Math. Mag. 48(4):223–225, 1975) in an infinite dimension using similar techniques as in (Shumrani et al. in SER Math. Inform. 33(2):197–202, 2018) and (Fogh, Behnamian and Pashaie in Int. J. Maps in Mathematics 2(41):1–13, 2019). As an application, we ensure the existence of solutions for infinite dimensional Fredholm integral equation and Uryshon type integral equation.https://doi.org/10.1186/s13662-021-03583-7Fixed pointGeraghty theoremComplete metric spaceInfinite dimensionH k $H_{k}$ contractionM k $M_{k}$ function |
| spellingShingle | R. Bardhan C. Ozel L. Guran H. Aydi Choonkil Park Infinite Geraghty type extensions and their applications on integral equations Advances in Difference Equations Fixed point Geraghty theorem Complete metric space Infinite dimension H k $H_{k}$ contraction M k $M_{k}$ function |
| title | Infinite Geraghty type extensions and their applications on integral equations |
| title_full | Infinite Geraghty type extensions and their applications on integral equations |
| title_fullStr | Infinite Geraghty type extensions and their applications on integral equations |
| title_full_unstemmed | Infinite Geraghty type extensions and their applications on integral equations |
| title_short | Infinite Geraghty type extensions and their applications on integral equations |
| title_sort | infinite geraghty type extensions and their applications on integral equations |
| topic | Fixed point Geraghty theorem Complete metric space Infinite dimension H k $H_{k}$ contraction M k $M_{k}$ function |
| url | https://doi.org/10.1186/s13662-021-03583-7 |
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