Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions
The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-11-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/11/2041 |
| _version_ | 1797547776721027072 |
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| author | Georgia Irina Oros |
| author_facet | Georgia Irina Oros |
| author_sort | Georgia Irina Oros |
| collection | DOAJ |
| description | The theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and have defined the differential superordination for harmonic complex-valued functions. Finding the best subordinant of a differential superordination is among the main purposes in this research subject. In this article, conditions for a harmonic complex-valued function p to be the best subordinant of a differential superordination for harmonic complex-valued functions are given. Examples are also provided to show how the theoretical findings can be used and also to prove the connection with the results obtained in 2015. |
| first_indexed | 2024-03-10T14:48:57Z |
| format | Article |
| id | doaj.art-90b4e0dee585468c9b634af26f17ab29 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T14:48:57Z |
| publishDate | 2020-11-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-90b4e0dee585468c9b634af26f17ab292023-11-20T21:09:56ZengMDPI AGMathematics2227-73902020-11-01811204110.3390/math8112041Best Subordinant for Differential Superordinations of Harmonic Complex-Valued FunctionsGeorgia Irina Oros0Department of Mathematics and Computer Sciences, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, RomaniaThe theory of differential subordinations has been extended from the analytic functions to the harmonic complex-valued functions in 2015. In a recent paper published in 2019, the authors have considered the dual problem of the differential subordination for the harmonic complex-valued functions and have defined the differential superordination for harmonic complex-valued functions. Finding the best subordinant of a differential superordination is among the main purposes in this research subject. In this article, conditions for a harmonic complex-valued function p to be the best subordinant of a differential superordination for harmonic complex-valued functions are given. Examples are also provided to show how the theoretical findings can be used and also to prove the connection with the results obtained in 2015.https://www.mdpi.com/2227-7390/8/11/2041differential subordinationdifferential superordinationharmonic functionanalytic functionsubordinantbest subordinant |
| spellingShingle | Georgia Irina Oros Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions Mathematics differential subordination differential superordination harmonic function analytic function subordinant best subordinant |
| title | Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions |
| title_full | Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions |
| title_fullStr | Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions |
| title_full_unstemmed | Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions |
| title_short | Best Subordinant for Differential Superordinations of Harmonic Complex-Valued Functions |
| title_sort | best subordinant for differential superordinations of harmonic complex valued functions |
| topic | differential subordination differential superordination harmonic function analytic function subordinant best subordinant |
| url | https://www.mdpi.com/2227-7390/8/11/2041 |
| work_keys_str_mv | AT georgiairinaoros bestsubordinantfordifferentialsuperordinationsofharmoniccomplexvaluedfunctions |