Some Properties for Subordinations of Analytic Functions
Let the class of functions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></mat...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-01-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/2/131 |
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| author | Hatun Özlem Güney Daniel Breaz Shigeyoshi Owa |
| author_facet | Hatun Özlem Güney Daniel Breaz Shigeyoshi Owa |
| author_sort | Hatun Özlem Güney |
| collection | DOAJ |
| description | Let the class of functions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></msubsup><msub><mi>a</mi><mi>k</mi></msub><msup><mi>z</mi><mi>k</mi></msup></mrow></semantics></math></inline-formula>, which are denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> and called analytic functions in the open-unit disk. There are many interesting properties of the functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> concerning the subordinations. Applying the three lemmas for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results. |
| first_indexed | 2024-03-11T09:09:48Z |
| format | Article |
| id | doaj.art-3cbb6aaeffb24839b368c45ec0df5e97 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-11T09:09:48Z |
| publishDate | 2023-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-3cbb6aaeffb24839b368c45ec0df5e972023-11-16T19:05:42ZengMDPI AGAxioms2075-16802023-01-0112213110.3390/axioms12020131Some Properties for Subordinations of Analytic FunctionsHatun Özlem Güney0Daniel Breaz1Shigeyoshi Owa2Department of Mathematics, Faculty of Science, Dicle University, 21280 Diyarbakır, TürkiyeDepartment of Exact Sciences and Engineering, “1 Decembrie 1918” University Alba Iulia, 510009 Alba Iulia, Romania“1 Decembrie 1918” University Alba Iulia, 510009 Alba-Iulia, RomaniaLet the class of functions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mi>z</mi><mo>+</mo><msubsup><mo>∑</mo><mrow><mi>k</mi><mo>=</mo><mn>2</mn></mrow><mo>∞</mo></msubsup><msub><mi>a</mi><mi>k</mi></msub><msup><mi>z</mi><mi>k</mi></msup></mrow></semantics></math></inline-formula>, which are denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> and called analytic functions in the open-unit disk. There are many interesting properties of the functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo></mrow></semantics></math></inline-formula> in the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> concerning the subordinations. Applying the three lemmas for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> provided by Miller and Mocanu and by Nunokawa, we consider many interesting properties of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>(</mo><mi>z</mi><mo>)</mo><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> with subordinations. Furthermore, we provide simple examples for our results. We think it is very important to consider examples of the results.https://www.mdpi.com/2075-1680/12/2/131analytic functionstarlike function of order αconvex function of order αsubordinationdifferential subordinaton |
| spellingShingle | Hatun Özlem Güney Daniel Breaz Shigeyoshi Owa Some Properties for Subordinations of Analytic Functions Axioms analytic function starlike function of order α convex function of order α subordination differential subordinaton |
| title | Some Properties for Subordinations of Analytic Functions |
| title_full | Some Properties for Subordinations of Analytic Functions |
| title_fullStr | Some Properties for Subordinations of Analytic Functions |
| title_full_unstemmed | Some Properties for Subordinations of Analytic Functions |
| title_short | Some Properties for Subordinations of Analytic Functions |
| title_sort | some properties for subordinations of analytic functions |
| topic | analytic function starlike function of order α convex function of order α subordination differential subordinaton |
| url | https://www.mdpi.com/2075-1680/12/2/131 |
| work_keys_str_mv | AT hatunozlemguney somepropertiesforsubordinationsofanalyticfunctions AT danielbreaz somepropertiesforsubordinationsofanalyticfunctions AT shigeyoshiowa somepropertiesforsubordinationsofanalyticfunctions |