Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities
In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using <inline-formula><math xmlns="http://www.w3...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/5/904 |
| _version_ | 1797533493401485312 |
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| author | Georgia Irina Oros |
| author_facet | Georgia Irina Oros |
| author_sort | Georgia Irina Oros |
| collection | DOAJ |
| description | In their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mo>ℝ</mo><mo>,</mo><mo> </mo><mi>c</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></mrow></semantics></math></inline-formula>. The study done in this paper extends the results on the univalence of the considered function taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mo>ℂ</mo><mo>,</mo></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></mrow></semantics></math></inline-formula> two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outcomes. Examples showing how the univalence results can be applied are also included. |
| first_indexed | 2024-03-10T11:16:18Z |
| format | Article |
| id | doaj.art-8f42843d39114145aa81830a9581ae67 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T11:16:18Z |
| publishDate | 2021-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-8f42843d39114145aa81830a9581ae672023-11-21T20:26:14ZengMDPI AGSymmetry2073-89942021-05-0113590410.3390/sym13050904Univalence Conditions for Gaussian Hypergeometric Function Involving Differential InequalitiesGeorgia Irina Oros0Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, RomaniaIn their paper published in 1990, Miller and Mocanu have investigated the special function Gaussian hypergeometric function in view of its relation to the theory of analytic functions, stating conditions for this function to be univalent using <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mo>ℝ</mo><mo>,</mo><mo> </mo><mi>c</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></mrow></semantics></math></inline-formula>. The study done in this paper extends the results on the univalence of the considered function taking <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>∈</mo><mo>ℂ</mo><mo>,</mo></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>c</mi><mo>≠</mo><mn>0</mn><mo>,</mo><mo>−</mo><mn>1</mn><mo>,</mo><mo>−</mo><mn>2</mn><mo>,</mo><mo>…</mo></mrow></semantics></math></inline-formula> two criteria being stated in the corollaries of the proved theorems. An interpretation of the univalence results from the sets inclusion view is also given, underlining the geometrical properties of the outcomes. Examples showing how the univalence results can be applied are also included.https://www.mdpi.com/2073-8994/13/5/904differential subordinationGaussian hypergeometric functiondifferential inequality in ℂ |
| spellingShingle | Georgia Irina Oros Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities Symmetry differential subordination Gaussian hypergeometric function differential inequality in ℂ |
| title | Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities |
| title_full | Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities |
| title_fullStr | Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities |
| title_full_unstemmed | Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities |
| title_short | Univalence Conditions for Gaussian Hypergeometric Function Involving Differential Inequalities |
| title_sort | univalence conditions for gaussian hypergeometric function involving differential inequalities |
| topic | differential subordination Gaussian hypergeometric function differential inequality in ℂ |
| url | https://www.mdpi.com/2073-8994/13/5/904 |
| work_keys_str_mv | AT georgiairinaoros univalenceconditionsforgaussianhypergeometricfunctioninvolvingdifferentialinequalities |