Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications
In this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial c...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2021/4564694 |
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| _version_ | 1832560542522277888 |
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| author | Mostafa Amani Rasoul Aghalary Ali Ebadian |
| author_facet | Mostafa Amani Rasoul Aghalary Ali Ebadian |
| author_sort | Mostafa Amani |
| collection | DOAJ |
| description | In this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial coefficients. Actually, by extending the Nunokawa lemma for fixed initial coefficient functions, we obtain some novel results on subclasses of univalent functions, such as differential inequalities for univalency or starlikeness of analytic functions. Also, we provide some new sufficient conditions for strongly starlike functions. The results of this paper extend and improve the previously known results by considering functions with fixed second coefficients. |
| format | Article |
| id | doaj-art-a4c8a759ad3042378e150abe5028a54e |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-a4c8a759ad3042378e150abe5028a54e2025-02-03T01:27:21ZengWileyJournal of Function Spaces2314-88962314-88882021-01-01202110.1155/2021/45646944564694Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its ApplicationsMostafa Amani0Rasoul Aghalary1Ali Ebadian2Department of Mathematics, Faculty of Science, Urmia University, Urmia, IranDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, IranDepartment of Mathematics, Faculty of Science, Urmia University, Urmia, IranIn this paper, we study some properties of analytic functions with fixed initial coefficients. The methodology of differential subordination is used for modification and improvements of several well-known results for subclasses of univalent functions by restricting the functions with fixed initial coefficients. Actually, by extending the Nunokawa lemma for fixed initial coefficient functions, we obtain some novel results on subclasses of univalent functions, such as differential inequalities for univalency or starlikeness of analytic functions. Also, we provide some new sufficient conditions for strongly starlike functions. The results of this paper extend and improve the previously known results by considering functions with fixed second coefficients.http://dx.doi.org/10.1155/2021/4564694 |
| spellingShingle | Mostafa Amani Rasoul Aghalary Ali Ebadian Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications Journal of Function Spaces |
| title | Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications |
| title_full | Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications |
| title_fullStr | Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications |
| title_full_unstemmed | Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications |
| title_short | Extension of Nunokawa Lemma for Functions with Fixed Second Coefficient and Its Applications |
| title_sort | extension of nunokawa lemma for functions with fixed second coefficient and its applications |
| url | http://dx.doi.org/10.1155/2021/4564694 |
| work_keys_str_mv | AT mostafaamani extensionofnunokawalemmaforfunctionswithfixedsecondcoefficientanditsapplications AT rasoulaghalary extensionofnunokawalemmaforfunctionswithfixedsecondcoefficientanditsapplications AT aliebadian extensionofnunokawalemmaforfunctionswithfixedsecondcoefficientanditsapplications |