Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator
We defined two new subclasses of analytic bi-univalent function class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>,</mo></mrow></semantics></math>...
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MDPI AG
2022-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/13/2241 |
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| author | Asma Alharbi Gangadharan Murugusundaramoorthy Sheza. M. El-Deeb |
| author_facet | Asma Alharbi Gangadharan Murugusundaramoorthy Sheza. M. El-Deeb |
| author_sort | Asma Alharbi |
| collection | DOAJ |
| description | We defined two new subclasses of analytic bi-univalent function class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>,</mo></mrow></semantics></math></inline-formula> in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>2</mn></msub><mrow><mo stretchy="false">|</mo><mo>,</mo><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>3</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>4</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> for the functions in these new subclasses of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Σ</mo></semantics></math></inline-formula> are investigated. Using the estimates of coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>, we also discuss the Fekete-Szegö inequality results for the function classes defined in this paper. Relevant connections of these results, presented here as corollaries, are new and not studied in association with Sălăgean-Erdély–Kober operator for the subclasses defined earlier. |
| first_indexed | 2024-03-09T04:02:48Z |
| format | Article |
| id | doaj.art-b14f2bad17d94baf87c2351e123072a0 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:02:48Z |
| publishDate | 2022-06-01 |
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| spelling | doaj.art-b14f2bad17d94baf87c2351e123072a02023-12-03T14:11:54ZengMDPI AGMathematics2227-73902022-06-011013224110.3390/math10132241Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober OperatorAsma Alharbi0Gangadharan Murugusundaramoorthy1Sheza. M. El-Deeb2Department of Mathematics, College of Science and Arts, ArRass, Qassim University, Buraidah 51452, Saudi ArabiaSchool of Advanced Sciences, Vellore Institute of Technology, Vellore 632014, TN, IndiaDepartment of Mathematics, Faculty of Science, Damietta University, New Damietta 34517, EgyptWe defined two new subclasses of analytic bi-univalent function class <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Σ</mo><mo>,</mo></mrow></semantics></math></inline-formula> in the open unit disk related with the Sălăgean–Erdély–Kober operator. The bounds on initial coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>2</mn></msub><mrow><mo stretchy="false">|</mo><mo>,</mo><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>3</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo stretchy="false">|</mo></mrow><msub><mi>a</mi><mn>4</mn></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> for the functions in these new subclasses of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Σ</mo></semantics></math></inline-formula> are investigated. Using the estimates of coefficients <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>a</mi><mn>2</mn></msub><mo>,</mo><msub><mi>a</mi><mn>3</mn></msub></mrow></semantics></math></inline-formula>, we also discuss the Fekete-Szegö inequality results for the function classes defined in this paper. Relevant connections of these results, presented here as corollaries, are new and not studied in association with Sălăgean-Erdély–Kober operator for the subclasses defined earlier.https://www.mdpi.com/2227-7390/10/13/2241univalent functionsanalytic functionsbi-univalent functionsSălăgean operatorErdély–Kober fractional-order derivativecoefficient bounds |
| spellingShingle | Asma Alharbi Gangadharan Murugusundaramoorthy Sheza. M. El-Deeb Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator Mathematics univalent functions analytic functions bi-univalent functions Sălăgean operator Erdély–Kober fractional-order derivative coefficient bounds |
| title | Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator |
| title_full | Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator |
| title_fullStr | Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator |
| title_full_unstemmed | Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator |
| title_short | Yamaguchi -Noshiro Type Bi-Univalent Functions Associated with Sălăgean-Erdély–Kober Operator |
| title_sort | yamaguchi noshiro type bi univalent functions associated with salagean erdely kober operator |
| topic | univalent functions analytic functions bi-univalent functions Sălăgean operator Erdély–Kober fractional-order derivative coefficient bounds |
| url | https://www.mdpi.com/2227-7390/10/13/2241 |
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