Coefficient Related Studies for New Classes of Bi-Univalent Functions
Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and b...
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MDPI AG
2020-07-01
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| Online Access: | https://www.mdpi.com/2227-7390/8/7/1110 |
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| author | Ágnes Orsolya Páll-Szabó Georgia Irina Oros |
| author_facet | Ágnes Orsolya Páll-Szabó Georgia Irina Oros |
| author_sort | Ágnes Orsolya Páll-Szabó |
| collection | DOAJ |
| description | Using the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>2</mn> </msub> </mfenced> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>3</mn> </msub> </mfenced> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>4</mn> </msub> </mfenced> </semantics> </math> </inline-formula> of the functions in the newly defined classes are given. Obtaining Fekete–Szegő inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete–Szegő functional is obtained for each of the three classes. |
| first_indexed | 2024-03-10T18:39:36Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T18:39:36Z |
| publishDate | 2020-07-01 |
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| series | Mathematics |
| spelling | doaj.art-7ade27a605924629a2a332408552669b2023-11-20T05:57:24ZengMDPI AGMathematics2227-73902020-07-0187111010.3390/math8071110Coefficient Related Studies for New Classes of Bi-Univalent FunctionsÁgnes Orsolya Páll-Szabó0Georgia Irina Oros1Faculty of Mathematics and Computer Science, Babes-Bolyai University, 400084 Cluj Napoca, RomaniaDepartment of Mathematics and Computer Sciences, Faculty of Informatics and Sciences, University of Oradea, 410087 Oradea, RomaniaUsing the recently introduced Sălăgean integro-differential operator, three new classes of bi-univalent functions are introduced in this paper. In the study of bi-univalent functions, estimates on the first two Taylor–Maclaurin coefficients are usually given. We go further in the present paper and bounds of the first three coefficients <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>2</mn> </msub> </mfenced> </semantics> </math> </inline-formula>, <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>3</mn> </msub> </mfenced> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mfenced separators="" open="|" close="|"> <msub> <mi>a</mi> <mn>4</mn> </msub> </mfenced> </semantics> </math> </inline-formula> of the functions in the newly defined classes are given. Obtaining Fekete–Szegő inequalities for different classes of functions is a topic of interest at this time as it will be shown later by citing recent papers. So, continuing the study on the coefficients of those classes, the well-known Fekete–Szegő functional is obtained for each of the three classes.https://www.mdpi.com/2227-7390/8/7/1110bi-univalent functionsSălăgean integral and differential operatorcoefficient boundsFekete–Szegő problem |
| spellingShingle | Ágnes Orsolya Páll-Szabó Georgia Irina Oros Coefficient Related Studies for New Classes of Bi-Univalent Functions Mathematics bi-univalent functions Sălăgean integral and differential operator coefficient bounds Fekete–Szegő problem |
| title | Coefficient Related Studies for New Classes of Bi-Univalent Functions |
| title_full | Coefficient Related Studies for New Classes of Bi-Univalent Functions |
| title_fullStr | Coefficient Related Studies for New Classes of Bi-Univalent Functions |
| title_full_unstemmed | Coefficient Related Studies for New Classes of Bi-Univalent Functions |
| title_short | Coefficient Related Studies for New Classes of Bi-Univalent Functions |
| title_sort | coefficient related studies for new classes of bi univalent functions |
| topic | bi-univalent functions Sălăgean integral and differential operator coefficient bounds Fekete–Szegő problem |
| url | https://www.mdpi.com/2227-7390/8/7/1110 |
| work_keys_str_mv | AT agnesorsolyapallszabo coefficientrelatedstudiesfornewclassesofbiunivalentfunctions AT georgiairinaoros coefficientrelatedstudiesfornewclassesofbiunivalentfunctions |