Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions
The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions <inline-formula><math xmlns="...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/14/2/427 |
| _version_ | 1797476355987734528 |
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| author | Alina Alb Lupaş Georgia Irina Oros |
| author_facet | Alina Alb Lupaş Georgia Irina Oros |
| author_sort | Alina Alb Lupaş |
| collection | DOAJ |
| description | The study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>n</mi></msub><mo>=</mo><mfenced separators="" open="{" close=""><mi>f</mi><mo>∈</mo><mi mathvariant="script">H</mi><mfenced open="(" close=")"><mi>U</mi></mfenced><mo>:</mo><mi>f</mi><mfenced open="(" close=")"><mi>z</mi></mfenced><mo>=</mo><mi>z</mi><mo>+</mo></mfenced></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="" close="}"><msub><mi>a</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mi>z</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>…</mo><mo>,</mo><mspace width="4.pt"></mspace><mi>z</mi><mo>∈</mo><mi>U</mi></mfenced></semantics></math></inline-formula> written simply <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the newly introduced class involves functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties. |
| first_indexed | 2024-03-09T20:57:43Z |
| format | Article |
| id | doaj.art-b3856c3a002a45ae9d22992f209f83ad |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-09T20:57:43Z |
| publishDate | 2022-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b3856c3a002a45ae9d22992f209f83ad2023-11-23T22:18:21ZengMDPI AGSymmetry2073-89942022-02-0114242710.3390/sym14020427Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic FunctionsAlina Alb Lupaş0Georgia Irina Oros1Department of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaDepartment of Mathematics and Computer Science, University of Oradea, 1 Universitatii Street, 410087 Oradea, RomaniaThe study on fractional integrals of confluent hypergeometric functions provides interesting subordination and superordination results and inspired the idea of using this operator to introduce a new class of analytic functions. Given the class of functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">A</mi><mi>n</mi></msub><mo>=</mo><mfenced separators="" open="{" close=""><mi>f</mi><mo>∈</mo><mi mathvariant="script">H</mi><mfenced open="(" close=")"><mi>U</mi></mfenced><mo>:</mo><mi>f</mi><mfenced open="(" close=")"><mi>z</mi></mfenced><mo>=</mo><mi>z</mi><mo>+</mo></mfenced></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mfenced separators="" open="" close="}"><msub><mi>a</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msub><msup><mi>z</mi><mrow><mi>n</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>+</mo><mo>…</mo><mo>,</mo><mspace width="4.pt"></mspace><mi>z</mi><mo>∈</mo><mi>U</mi></mfenced></semantics></math></inline-formula> written simply <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">A</mi></semantics></math></inline-formula> when <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula>, the newly introduced class involves functions <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>∈</mo><mi mathvariant="script">A</mi></mrow></semantics></math></inline-formula> considered in the study due to their special properties. The aim of this paper is to present the outcomes of the study performed on the new class, which include a coefficient inequality, a distortion theorem and extreme points of the class. The starlikeness and convexity properties of this class are also discussed, and partial sums of functions from the class are evaluated in order to obtain class boundary properties.https://www.mdpi.com/2073-8994/14/2/427analytic functioncoefficient inequalitypartial sumstarlike functionconvex functionfractional integral |
| spellingShingle | Alina Alb Lupaş Georgia Irina Oros Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions Symmetry analytic function coefficient inequality partial sum starlike function convex function fractional integral |
| title | Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions |
| title_full | Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions |
| title_fullStr | Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions |
| title_full_unstemmed | Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions |
| title_short | Fractional Integral of a Confluent Hypergeometric Function Applied to Defining a New Class of Analytic Functions |
| title_sort | fractional integral of a confluent hypergeometric function applied to defining a new class of analytic functions |
| topic | analytic function coefficient inequality partial sum starlike function convex function fractional integral |
| url | https://www.mdpi.com/2073-8994/14/2/427 |
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