Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions
The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its n...
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MDPI AG
2022-01-01
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| author | Georgia Irina Oros Luminiţa-Ioana Cotîrlă |
| author_facet | Georgia Irina Oros Luminiţa-Ioana Cotîrlă |
| author_sort | Georgia Irina Oros |
| collection | DOAJ |
| description | The results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin 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><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></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><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes. |
| first_indexed | 2024-03-10T03:31:36Z |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:31:36Z |
| publishDate | 2022-01-01 |
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| series | Mathematics |
| spelling | doaj.art-24c0ce57ee294ac18b6be5887a0781152023-11-23T11:54:35ZengMDPI AGMathematics2227-73902022-01-0110112910.3390/math10010129Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent FunctionsGeorgia Irina Oros0Luminiţa-Ioana Cotîrlă1Department of Mathematics and Computer Science, University of Oradea, 410087 Oradea, RomaniaDepartment of Mathematics, Technical University of Cluj-Napoca, 400114 Cluj-Napoca, RomaniaThe results presented in this paper deal with the classical but still prevalent problem of introducing new classes of m-fold symmetric bi-univalent functions and studying properties related to coefficient estimates. Quantum calculus aspects are also considered in this study in order to enhance its novelty and to obtain more interesting results. We present three new classes of bi-univalent functions, generalizing certain previously studied classes. The relation between the known results and the new ones presented here is highlighted. Estimates on the Taylor–Maclaurin 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><mrow><mi>m</mi><mo>+</mo><mn>1</mn></mrow></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><mrow><mn>2</mn><mi>m</mi><mo>+</mo><mn>1</mn></mrow></msub><mrow><mo stretchy="false">|</mo></mrow></mrow></semantics></math></inline-formula> are obtained and, furthermore, the much investigated aspect of Fekete–Szegő functional is also considered for each of the new classes.https://www.mdpi.com/2227-7390/10/1/129<i>m</i>-fold symmetricbi-univalent functionsanalytic functionsFekete–Szegö functionalcoefficient boundscoefficient estimates |
| spellingShingle | Georgia Irina Oros Luminiţa-Ioana Cotîrlă Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions Mathematics <i>m</i>-fold symmetric bi-univalent functions analytic functions Fekete–Szegö functional coefficient bounds coefficient estimates |
| title | Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_full | Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_fullStr | Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_full_unstemmed | Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_short | Coefficient Estimates and the Fekete–Szegö Problem for New Classes of <i>m</i>-Fold Symmetric Bi-Univalent Functions |
| title_sort | coefficient estimates and the fekete szego problem for new classes of i m i fold symmetric bi univalent functions |
| topic | <i>m</i>-fold symmetric bi-univalent functions analytic functions Fekete–Szegö functional coefficient bounds coefficient estimates |
| url | https://www.mdpi.com/2227-7390/10/1/129 |
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