Year 2019,
Volume: 32 Issue: 2, 637 - 647, 01.06.2019
Ebrahim Analouei Adegani
,
Ahmad Zıreh
Mostafa Jafarı
References
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- Reference3 H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006) 179-222.
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- Reference14 W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, 157–169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA, 1994.
- Reference15 H. M. Srivastava, S. S. Eker and R. M. Ali, Coeffcient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29 (2015) 1839-1845
- Reference16 H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett., 23 (2010) 1188-1192.
- Reference17 S. Sivasubramanian, R. Sivakumar, S. Kanas and Seong-A Kim, Verification of Brannan and Clunie's conjecture for certain subclasses of bi univalent functions, Ann. Pol. Math., 113 (2015) 295-303.
- Reference18 P. G. Todorov, On the Faber polynomials of the univalent functions of class, J. Math. Anal. Appl., 162 (1991) 268-276.
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- Reference20 A. Zireh, E. Analouei Adegani and S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic
bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23 (2016) 487-504.
Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination
Year 2019,
Volume: 32 Issue: 2, 637 - 647, 01.06.2019
Ebrahim Analouei Adegani
,
Ahmad Zıreh
Mostafa Jafarı
Abstract
In this work, the Faber polynomial expansions and
a different method were employed to estimate the coefficients of a subclass of
bi-close-to-convex functions, which is introduced by subordination concept in
the open unit disk. Further, we generalize some of the previous outcomes.
References
- Reference1 H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006) 179-222.
- Reference2 H. Airault and J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math., 126 (2002) 343-367.
- Reference3 H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math., 130 (2006) 179-222.
- Reference4 R. M. Ali, S. K. Lee, V. Ravichandran and S. Subramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett., 25 (2012) 344-351.
- Reference5 S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R. Acad. Sci. Paris, 352 (2014) 479-484.
- Reference6 P. L. Duren, Univalent Functions, Springer-Verlag, New York, Berlin, 1983.
- Reference7 G. Faber, Uber polynomische Entwickelungen, Math. Ann., 57 (1903) 389-408.
- Reference8 B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011) 1569-1573.
- Reference9 S. G. Hamidi and J. M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Math. Acad. Sci. Paris, 352 (2014) 17-20..
- Reference10 S. G. Hamidi and J. M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Math. Acad. Sci. Paris, 354 (2016) 365-370.
- Reference11 S. G. Hamidi, S. A. Halim and J. M. Jahangiri, Coefficient estimates for a class of meromorphic bi-univalent functions, C. R. Math. Acad. Sci. Paris, 351 (2013) 349-352.
- Reference12 W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J., 1 (1952) 169–185.
- Reference13 M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18 (1967) 63-68.
- Reference14 W. C. Ma and D. Minda, A unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Tianjin, 1992, 157–169, Conf. Proc. Lecture Notes Anal., I, Int. Press, Cambridge, MA, 1994.
- Reference15 H. M. Srivastava, S. S. Eker and R. M. Ali, Coeffcient bounds for a certain class of analytic and bi-univalent functions, Filomat, 29 (2015) 1839-1845
- Reference16 H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett., 23 (2010) 1188-1192.
- Reference17 S. Sivasubramanian, R. Sivakumar, S. Kanas and Seong-A Kim, Verification of Brannan and Clunie's conjecture for certain subclasses of bi univalent functions, Ann. Pol. Math., 113 (2015) 295-303.
- Reference18 P. G. Todorov, On the Faber polynomials of the univalent functions of class, J. Math. Anal. Appl., 162 (1991) 268-276.
- Reference19 A. Zireh and E. Analouei Adegani, Coefficient estimates for a subclass of analytic and bi-univalent functions, Bull. Iranian Math. Soc., 42 (2016) 881-889.
- Reference20 A. Zireh, E. Analouei Adegani and S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic
bi-univalent functions defined by subordination, Bull. Belg. Math. Soc. Simon Stevin, 23 (2016) 487-504.