On Classes of Meromorphic Functions Defined by Subordination and Convolution
For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup>&l...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-09-01
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| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/15/9/1763 |
| _version_ | 1797576562939265024 |
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| author | Luminiţa-Ioana Cotîrlă Elisabeta-Alina Totoi |
| author_facet | Luminiţa-Ioana Cotîrlă Elisabeta-Alina Totoi |
| author_sort | Luminiţa-Ioana Cotîrlă |
| collection | DOAJ |
| description | For <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup></mrow></semantics></math></inline-formula>, let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula> denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><mi>b</mi></mrow><mi>n</mi></msubsup></semantics></math></inline-formula>, which generalizes some previously studied operators. We introduce some new subclasses of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula>, associated with subordination using the above operator, and we prove that these classes are preserved regarding the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub></semantics></math></inline-formula>, so we have symmetry when we look at the form of the class in which we consider the function <i>g</i> and at the form of the class of the image <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mrow><mfrac><mrow><mi>γ</mi><mo>−</mo><mi>p</mi></mrow><msup><mi>z</mi><mi>γ</mi></msup></mfrac><msubsup><mo>∫</mo><mn>0</mn><mi>z</mi></msubsup><mi>g</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mi>t</mi><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>d</mi><mi>t</mi></mrow></mstyle></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Re</mi><mspace width="0.166667em"></mspace><mi>γ</mi><mo>></mo><mi>p</mi></mrow></semantics></math></inline-formula>. |
| first_indexed | 2024-03-10T21:54:49Z |
| format | Article |
| id | doaj.art-b7f0823d4b284202966e5223a129a301 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T21:54:49Z |
| publishDate | 2023-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b7f0823d4b284202966e5223a129a3012023-11-19T13:12:20ZengMDPI AGSymmetry2073-89942023-09-01159176310.3390/sym15091763On Classes of Meromorphic Functions Defined by Subordination and ConvolutionLuminiţa-Ioana Cotîrlă0Elisabeta-Alina Totoi1Department of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaDepartment of Mathematics and Informatics, Lucian Blaga University of Sibiu, 550012 Sibiu, RomaniaFor <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>∈</mo><msup><mi mathvariant="double-struck">N</mi><mo>*</mo></msup></mrow></semantics></math></inline-formula>, let <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula> denote the class of meromorphic p-valent functions. We consider an operator for meromorphic functions denoted by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msubsup><mi>T</mi><mrow><mi>b</mi></mrow><mi>n</mi></msubsup></semantics></math></inline-formula>, which generalizes some previously studied operators. We introduce some new subclasses of the class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mo>Σ</mo><mi>p</mi></msub></semantics></math></inline-formula>, associated with subordination using the above operator, and we prove that these classes are preserved regarding the operator <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub></semantics></math></inline-formula>, so we have symmetry when we look at the form of the class in which we consider the function <i>g</i> and at the form of the class of the image <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula>, where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>J</mi><mrow><mi>p</mi><mo>,</mo><mi>γ</mi></mrow></msub><mrow><mo>(</mo><mi>g</mi><mo>)</mo></mrow><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow><mo>=</mo><mstyle scriptlevel="0" displaystyle="true"><mrow><mfrac><mrow><mi>γ</mi><mo>−</mo><mi>p</mi></mrow><msup><mi>z</mi><mi>γ</mi></msup></mfrac><msubsup><mo>∫</mo><mn>0</mn><mi>z</mi></msubsup><mi>g</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><msup><mi>t</mi><mrow><mi>γ</mi><mo>−</mo><mn>1</mn></mrow></msup><mi>d</mi><mi>t</mi></mrow></mstyle></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>γ</mi><mo>∈</mo><mi mathvariant="double-struck">C</mi></mrow></semantics></math></inline-formula> with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Re</mi><mspace width="0.166667em"></mspace><mi>γ</mi><mo>></mo><mi>p</mi></mrow></semantics></math></inline-formula>.https://www.mdpi.com/2073-8994/15/9/1763convolutionmeromorphic functionsintegral operatorsubordination |
| spellingShingle | Luminiţa-Ioana Cotîrlă Elisabeta-Alina Totoi On Classes of Meromorphic Functions Defined by Subordination and Convolution Symmetry convolution meromorphic functions integral operator subordination |
| title | On Classes of Meromorphic Functions Defined by Subordination and Convolution |
| title_full | On Classes of Meromorphic Functions Defined by Subordination and Convolution |
| title_fullStr | On Classes of Meromorphic Functions Defined by Subordination and Convolution |
| title_full_unstemmed | On Classes of Meromorphic Functions Defined by Subordination and Convolution |
| title_short | On Classes of Meromorphic Functions Defined by Subordination and Convolution |
| title_sort | on classes of meromorphic functions defined by subordination and convolution |
| topic | convolution meromorphic functions integral operator subordination |
| url | https://www.mdpi.com/2073-8994/15/9/1763 |
| work_keys_str_mv | AT luminitaioanacotirla onclassesofmeromorphicfunctionsdefinedbysubordinationandconvolution AT elisabetaalinatotoi onclassesofmeromorphicfunctionsdefinedbysubordinationandconvolution |