ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS
In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
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| Published in | Acta mathematica scientia Vol. 34; no. 1; pp. 228 - 240 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
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Elsevier Ltd
2014
Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China |
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| Abstract | In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors. |
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| AbstractList | In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors. In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors. |
| Author | 彭志刚 韩秋秋 |
| AuthorAffiliation | Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China |
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| Cites_doi | 10.1016/j.jmaa.2008.11.025 10.1007/BF00247676 10.1016/j.camwa.2011.05.041 10.1016/j.aml.2010.08.004 10.1016/j.aml.2011.09.012 10.1016/j.aml.2011.03.048 10.1016/j.amc.2011.01.055 10.1016/j.aml.2010.05.009 10.1016/j.aml.2011.11.013 10.1090/S0002-9939-1967-0206255-1 |
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| Keywords | 30C45 30C50 bi-univalent function coefficient 30C80 univalent function subordination coeffcient |
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| Notes | coefficient; univalent function; bi-univalent function; subordination In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors. Zhigang PENG Qiuqiu HAN Faculty of Mathematics and Computer Science, Hubei University, Wuhan 430062, China 42-1227/O ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23 |
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| References | Xu, Gui, Srivastava (bib15) 2012; 25 Ali, Lee, Ravichandran (bib18) 2012; 25 Lewin (bib11) 1967; 18 Brannan, Clunie (bib12) 1980 Aouf, Dziok, Sokol (bib5) 2011; 24 Mocanu (bib1) 1969; 11 Miller, Mocanu, Reade (bib2) 1973; 37 Duren (bib10) 1983 Sokol (bib6) 2011; 62 Lewandowski, Miller, Zlotkiewicz (bib3) 1974; 28 Ali (bib7) 2003; 26 Ma, Minda (bib8) 1994 Frasin, Aouf (bib17) 2011; 24 Netanyahu (bib13) 1969; 32 Badghaish, Ali, Ravichandran (bib9) 2011; 218 Brannan, Taha (bib14) 1986; 31 Sokol (bib4) 2009; 352 Srivastava, Mishra, Gochhayat (bib16) 2010; 23 Sokol (10.1016/S0252-9602(13)60140-X_bib4) 2009; 352 Brannan (10.1016/S0252-9602(13)60140-X_bib12) 1980 Miller (10.1016/S0252-9602(13)60140-X_bib2) 1973; 37 Badghaish (10.1016/S0252-9602(13)60140-X_bib9) 2011; 218 Lewin (10.1016/S0252-9602(13)60140-X_bib11) 1967; 18 Duren (10.1016/S0252-9602(13)60140-X_bib10) 1983 Lewandowski (10.1016/S0252-9602(13)60140-X_bib3) 1974; 28 Xu (10.1016/S0252-9602(13)60140-X_bib15) 2012; 25 Brannan (10.1016/S0252-9602(13)60140-X_bib14) 1986; 31 Srivastava (10.1016/S0252-9602(13)60140-X_bib16) 2010; 23 Aouf (10.1016/S0252-9602(13)60140-X_bib5) 2011; 24 Ali (10.1016/S0252-9602(13)60140-X_bib18) 2012; 25 Mocanu (10.1016/S0252-9602(13)60140-X_bib1) 1969; 11 Sokol (10.1016/S0252-9602(13)60140-X_bib6) 2011; 62 Ali (10.1016/S0252-9602(13)60140-X_bib7) 2003; 26 Frasin (10.1016/S0252-9602(13)60140-X_bib17) 2011; 24 Netanyahu (10.1016/S0252-9602(13)60140-X_bib13) 1969; 32 Ma (10.1016/S0252-9602(13)60140-X_bib8) 1994 |
| References_xml | – volume: 28 start-page: 53 year: 1974 end-page: 58 ident: bib3 article-title: Gamma-starlike functions publication-title: Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia – volume: 24 start-page: 1569 year: 2011 end-page: 1573 ident: bib17 article-title: New subclasses of bi-univalent functions publication-title: Appl Math Lett – volume: 25 start-page: 990 year: 2012 end-page: 994 ident: bib15 article-title: Coefficient estimates for a certain subclass of analytic and bi-univalent functions publication-title: Appl Math Lett – volume: 11 start-page: 127 year: 1969 end-page: 133 ident: bib1 article-title: Une propriete de convexite generalisee dans la theorie de la representation conforme publication-title: Mathematica (Cluj) – volume: 25 start-page: 344 year: 2012 end-page: 351 ident: bib18 article-title: Shamani Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions publication-title: Appl Math Lett – volume: 26 start-page: 63 year: 2003 end-page: 71 ident: bib7 article-title: Coefficients of the inverse of strongly starlike functions publication-title: Bull Malaysian Math Sci Soc – volume: 23 start-page: 1188 year: 2010 end-page: 1192 ident: bib16 article-title: Certain subclasses of analytic and bi-univalent functions publication-title: Appl Math Lett – volume: 62 start-page: 611 year: 2011 end-page: 619 ident: bib6 article-title: A certain class of starlike functions publication-title: Comput Math Appl – volume: 31 start-page: 70 year: 1986 end-page: 77 ident: bib14 article-title: On some classes of bi-univalent functions publication-title: Studia Univ Babes-Bolyai Math – year: 1980 ident: bib12 publication-title: Aspects of Contemporary Complex Analysis (Proceedings of the NATO Advanced Study Instute Held at the University of Durham, Durham: July 1-20, 1979) – start-page: 157 year: 1994 end-page: 169 ident: bib8 article-title: A unified treatment of some special classes of univalent functions publication-title: Proceedings of the Conference on Complex Analysis (Tianjin, 1992). Conf Proc Lecture Notes Anal I – volume: 37 start-page: 553 year: 1973 end-page: 554 ident: bib2 article-title: All α-convex functions are univalent and starlike publication-title: Proc Amer Math Soc – volume: 218 start-page: 667 year: 2011 end-page: 672 ident: bib9 article-title: Closure properties of operators on the Ma-Minda type starlike and convex functions publication-title: Appl Math Comp – volume: 32 start-page: 100 year: 1969 end-page: 112 ident: bib13 article-title: The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in | publication-title: Arch Rational Mech Anal – year: 1983 ident: bib10 publication-title: Univalent Functions – volume: 18 start-page: 63 year: 1967 end-page: 68 ident: bib11 article-title: On a coefficient problem for bi-univalent functions publication-title: Proc Amer Math Soc – volume: 24 start-page: 27 year: 2011 end-page: 32 ident: bib5 article-title: On a subclass of strongly starlike functions publication-title: Appl Math Lett – volume: 352 start-page: 696 year: 2009 end-page: 701 ident: bib4 article-title: On a condition for α-starlikeness publication-title: J Math Anal Appl – year: 1983 ident: 10.1016/S0252-9602(13)60140-X_bib10 – volume: 352 start-page: 696 year: 2009 ident: 10.1016/S0252-9602(13)60140-X_bib4 article-title: On a condition for α-starlikeness publication-title: J Math Anal Appl doi: 10.1016/j.jmaa.2008.11.025 – volume: 31 start-page: 70 issue: 2 year: 1986 ident: 10.1016/S0252-9602(13)60140-X_bib14 article-title: On some classes of bi-univalent functions publication-title: Studia Univ Babes-Bolyai Math – volume: 28 start-page: 53 year: 1974 ident: 10.1016/S0252-9602(13)60140-X_bib3 article-title: Gamma-starlike functions publication-title: Annales Universitatis Mariae Curie-Sklodowska Lublin-Polonia – year: 1980 ident: 10.1016/S0252-9602(13)60140-X_bib12 – volume: 32 start-page: 100 year: 1969 ident: 10.1016/S0252-9602(13)60140-X_bib13 article-title: The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1 publication-title: Arch Rational Mech Anal doi: 10.1007/BF00247676 – volume: 62 start-page: 611 year: 2011 ident: 10.1016/S0252-9602(13)60140-X_bib6 article-title: A certain class of starlike functions publication-title: Comput Math Appl doi: 10.1016/j.camwa.2011.05.041 – volume: 24 start-page: 27 year: 2011 ident: 10.1016/S0252-9602(13)60140-X_bib5 article-title: On a subclass of strongly starlike functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2010.08.004 – start-page: 157 year: 1994 ident: 10.1016/S0252-9602(13)60140-X_bib8 article-title: A unified treatment of some special classes of univalent functions – volume: 25 start-page: 344 year: 2012 ident: 10.1016/S0252-9602(13)60140-X_bib18 article-title: Shamani Supramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2011.09.012 – volume: 26 start-page: 63 year: 2003 ident: 10.1016/S0252-9602(13)60140-X_bib7 article-title: Coefficients of the inverse of strongly starlike functions publication-title: Bull Malaysian Math Sci Soc – volume: 24 start-page: 1569 year: 2011 ident: 10.1016/S0252-9602(13)60140-X_bib17 article-title: New subclasses of bi-univalent functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2011.03.048 – volume: 218 start-page: 667 year: 2011 ident: 10.1016/S0252-9602(13)60140-X_bib9 article-title: Closure properties of operators on the Ma-Minda type starlike and convex functions publication-title: Appl Math Comp doi: 10.1016/j.amc.2011.01.055 – volume: 23 start-page: 1188 year: 2010 ident: 10.1016/S0252-9602(13)60140-X_bib16 article-title: Certain subclasses of analytic and bi-univalent functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2010.05.009 – volume: 11 start-page: 127 year: 1969 ident: 10.1016/S0252-9602(13)60140-X_bib1 article-title: Une propriete de convexite generalisee dans la theorie de la representation conforme publication-title: Mathematica (Cluj) – volume: 25 start-page: 990 year: 2012 ident: 10.1016/S0252-9602(13)60140-X_bib15 article-title: Coefficient estimates for a certain subclass of analytic and bi-univalent functions publication-title: Appl Math Lett doi: 10.1016/j.aml.2011.11.013 – volume: 37 start-page: 553 year: 1973 ident: 10.1016/S0252-9602(13)60140-X_bib2 article-title: All α-convex functions are univalent and starlike publication-title: Proc Amer Math Soc – volume: 18 start-page: 63 year: 1967 ident: 10.1016/S0252-9602(13)60140-X_bib11 article-title: On a coefficient problem for bi-univalent functions publication-title: Proc Amer Math Soc doi: 10.1090/S0002-9939-1967-0206255-1 |
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| SubjectTerms | 30C45 30C50 30C80 bi-univalent function coefficient Functions (mathematics) Mathematical analysis subordination univalent function 分子 单叶函数 数学 物理学 |
| Title | ON THE COEFFICIENTS OF SEVERAL CLASSES OF BI-UNIVALENT FUNCTIONS |
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