On the characterization properties of certain hypergeometric functions in the open unit disk
Abstract Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z 1 F 2 ( a ; b , c ; z ) $z{}_{1}F_{2}(a;b,c;z)$ in the open unit disk. The usefulness of the main results for some f...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-12-01
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| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-022-02902-0 |
| _version_ | 1797973452896862208 |
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| author | Deepak Bansal Ravinder Krishna Raina Sudhananda Maharana Nak Eun Cho |
| author_facet | Deepak Bansal Ravinder Krishna Raina Sudhananda Maharana Nak Eun Cho |
| author_sort | Deepak Bansal |
| collection | DOAJ |
| description | Abstract Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z 1 F 2 ( a ; b , c ; z ) $z{}_{1}F_{2}(a;b,c;z)$ in the open unit disk. The usefulness of the main results for some familiar special functions like the modified Sturve function, the modified Lommel function, the modified Bessel function, and the F 1 0 ( − ; c ; z ) ${}_{0}F_{1}(-;c;z)$ function are also mentioned. We further consider a boundedness property of the function F 2 1 ( a ; b , c ; z ) $_{1}F_{2}(a;b,c;z)$ in the Hardy space of analytic functions. Several corollaries and special cases of the main results are also pointed out. |
| first_indexed | 2024-04-11T04:04:31Z |
| format | Article |
| id | doaj.art-ce32bd84804e421da3582fef837f550a |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-11T04:04:31Z |
| publishDate | 2022-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-ce32bd84804e421da3582fef837f550a2023-01-01T12:30:03ZengSpringerOpenJournal of Inequalities and Applications1029-242X2022-12-012022111610.1186/s13660-022-02902-0On the characterization properties of certain hypergeometric functions in the open unit diskDeepak Bansal0Ravinder Krishna Raina1Sudhananda Maharana2Nak Eun Cho3Department of Mathematics, University College of Engineering and TechnologyMaharana Pratap University of Agriculture and TechnologyDepartment of Mathematics, NIST (Autonomous)Department of Applied Mathematics, Pukyong National UniversityAbstract Our purpose in the present investigation is to study certain geometric properties such as the close-to-convexity, convexity, and starlikeness of the hypergeometric function z 1 F 2 ( a ; b , c ; z ) $z{}_{1}F_{2}(a;b,c;z)$ in the open unit disk. The usefulness of the main results for some familiar special functions like the modified Sturve function, the modified Lommel function, the modified Bessel function, and the F 1 0 ( − ; c ; z ) ${}_{0}F_{1}(-;c;z)$ function are also mentioned. We further consider a boundedness property of the function F 2 1 ( a ; b , c ; z ) $_{1}F_{2}(a;b,c;z)$ in the Hardy space of analytic functions. Several corollaries and special cases of the main results are also pointed out.https://doi.org/10.1186/s13660-022-02902-0Lommel functionSturve functionBessel functionAnalytic univalent functionStarlike functionClose-to-convex function |
| spellingShingle | Deepak Bansal Ravinder Krishna Raina Sudhananda Maharana Nak Eun Cho On the characterization properties of certain hypergeometric functions in the open unit disk Journal of Inequalities and Applications Lommel function Sturve function Bessel function Analytic univalent function Starlike function Close-to-convex function |
| title | On the characterization properties of certain hypergeometric functions in the open unit disk |
| title_full | On the characterization properties of certain hypergeometric functions in the open unit disk |
| title_fullStr | On the characterization properties of certain hypergeometric functions in the open unit disk |
| title_full_unstemmed | On the characterization properties of certain hypergeometric functions in the open unit disk |
| title_short | On the characterization properties of certain hypergeometric functions in the open unit disk |
| title_sort | on the characterization properties of certain hypergeometric functions in the open unit disk |
| topic | Lommel function Sturve function Bessel function Analytic univalent function Starlike function Close-to-convex function |
| url | https://doi.org/10.1186/s13660-022-02902-0 |
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