Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions
In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be <i>p</i>-valent functions. This work also extends the findings of Nunokawa and others.
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-03-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/3/295 |
| _version_ | 1797613527860510720 |
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| author | Lei Shi Muhammad Arif Syed Zakar Hussain Bukhari Malik Ali Raza |
| author_facet | Lei Shi Muhammad Arif Syed Zakar Hussain Bukhari Malik Ali Raza |
| author_sort | Lei Shi |
| collection | DOAJ |
| description | In the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be <i>p</i>-valent functions. This work also extends the findings of Nunokawa and others. |
| first_indexed | 2024-03-11T06:57:00Z |
| format | Article |
| id | doaj.art-f947fcc1e08647059d3ab709a39f970b |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T06:57:00Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-f947fcc1e08647059d3ab709a39f970b2023-11-17T09:35:30ZengMDPI AGAxioms2075-16802023-03-0112329510.3390/axioms12030295Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic FunctionsLei Shi0Muhammad Arif1Syed Zakar Hussain Bukhari2Malik Ali Raza3School of Mathematics and Statistics, Anyang Normal University, Anyang 455002, ChinaDepartment of Mathematics, Abdul Wali khan University Mardan, Mardan 23200, PakistanDepartment of Mathematics, Mirpur University of Science and Technology, Mirpur 10250, PakistanDepartment of Mathematics, Mirpur University of Science and Technology, Mirpur 10250, PakistanIn the present paper, we develop some implications leading to Carathéodory functions in the open disk and provide some new conditions for functions to be <i>p</i>-valent functions. This work also extends the findings of Nunokawa and others.https://www.mdpi.com/2075-1680/12/3/295multivalent functions<i>p</i>-valent functionsCarathéodory functions |
| spellingShingle | Lei Shi Muhammad Arif Syed Zakar Hussain Bukhari Malik Ali Raza Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions Axioms multivalent functions <i>p</i>-valent functions Carathéodory functions |
| title | Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions |
| title_full | Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions |
| title_fullStr | Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions |
| title_full_unstemmed | Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions |
| title_short | Some New Sufficient Conditions on <i>p</i>-Valency for Certain Analytic Functions |
| title_sort | some new sufficient conditions on i p i valency for certain analytic functions |
| topic | multivalent functions <i>p</i>-valent functions Carathéodory functions |
| url | https://www.mdpi.com/2075-1680/12/3/295 |
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