Certain Geometric Properties of the Fox–Wright Functions
The primary objective of this study is to establish necessary conditions so that the normalized Fox–Wright functions possess certain geometric properties, such as convexity and pre-starlikeness. In addition, we present a linear operator associated with the Fox–Wright functions and discuss its <i&...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-11-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/11/11/629 |
| _version_ | 1797469050770554880 |
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| author | Anish Kumar Saiful R. Mondal Sourav Das |
| author_facet | Anish Kumar Saiful R. Mondal Sourav Das |
| author_sort | Anish Kumar |
| collection | DOAJ |
| description | The primary objective of this study is to establish necessary conditions so that the normalized Fox–Wright functions possess certain geometric properties, such as convexity and pre-starlikeness. In addition, we present a linear operator associated with the Fox–Wright functions and discuss its <i>k</i>-uniform convexity and <i>k</i>-uniform starlikeness. Furthermore, some sufficient conditions were obtained so that this function belongs to the Hardy spaces. The results of this work are presumably new and illustrated by several consequences, remarks, and examples. |
| first_indexed | 2024-03-09T19:15:58Z |
| format | Article |
| id | doaj.art-3d7bad3275cd4e74ab3668759b241e58 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-09T19:15:58Z |
| publishDate | 2022-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3d7bad3275cd4e74ab3668759b241e582023-11-24T03:44:33ZengMDPI AGAxioms2075-16802022-11-01111162910.3390/axioms11110629Certain Geometric Properties of the Fox–Wright FunctionsAnish Kumar0Saiful R. Mondal1Sourav Das2Department of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, Jharkhand, IndiaDepartment of Mathematics and Statistics, College of Science, King Faisal University, Al Hasa 31982, Saudi ArabiaDepartment of Mathematics, National Institute of Technology Jamshedpur, Jamshedpur 831014, Jharkhand, IndiaThe primary objective of this study is to establish necessary conditions so that the normalized Fox–Wright functions possess certain geometric properties, such as convexity and pre-starlikeness. In addition, we present a linear operator associated with the Fox–Wright functions and discuss its <i>k</i>-uniform convexity and <i>k</i>-uniform starlikeness. Furthermore, some sufficient conditions were obtained so that this function belongs to the Hardy spaces. The results of this work are presumably new and illustrated by several consequences, remarks, and examples.https://www.mdpi.com/2075-1680/11/11/629Fox–Wright functionsanalytic functionsunivalent functionsconvex functionsstarlike functionsHardy spaces |
| spellingShingle | Anish Kumar Saiful R. Mondal Sourav Das Certain Geometric Properties of the Fox–Wright Functions Axioms Fox–Wright functions analytic functions univalent functions convex functions starlike functions Hardy spaces |
| title | Certain Geometric Properties of the Fox–Wright Functions |
| title_full | Certain Geometric Properties of the Fox–Wright Functions |
| title_fullStr | Certain Geometric Properties of the Fox–Wright Functions |
| title_full_unstemmed | Certain Geometric Properties of the Fox–Wright Functions |
| title_short | Certain Geometric Properties of the Fox–Wright Functions |
| title_sort | certain geometric properties of the fox wright functions |
| topic | Fox–Wright functions analytic functions univalent functions convex functions starlike functions Hardy spaces |
| url | https://www.mdpi.com/2075-1680/11/11/629 |
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