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Year 2019, Volume: 32 Issue: 2, 637 - 647, 01.06.2019

Abstract

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.

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

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.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Mathematics
Authors

Ebrahim Analouei Adegani

Ahmad Zıreh This is me

Mostafa Jafarı This is me

Publication Date June 1, 2019
Published in Issue Year 2019 Volume: 32 Issue: 2

Cite

APA Analouei Adegani, E., Zıreh, A., & Jafarı, M. (2019). Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination. Gazi University Journal of Science, 32(2), 637-647.
AMA Analouei Adegani E, Zıreh A, Jafarı M. Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination. Gazi University Journal of Science. June 2019;32(2):637-647.
Chicago Analouei Adegani, Ebrahim, Ahmad Zıreh, and Mostafa Jafarı. “Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination”. Gazi University Journal of Science 32, no. 2 (June 2019): 637-47.
EndNote Analouei Adegani E, Zıreh A, Jafarı M (June 1, 2019) Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination. Gazi University Journal of Science 32 2 637–647.
IEEE E. Analouei Adegani, A. Zıreh, and M. Jafarı, “Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination”, Gazi University Journal of Science, vol. 32, no. 2, pp. 637–647, 2019.
ISNAD Analouei Adegani, Ebrahim et al. “Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination”. Gazi University Journal of Science 32/2 (June 2019), 637-647.
JAMA Analouei Adegani E, Zıreh A, Jafarı M. Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination. Gazi University Journal of Science. 2019;32:637–647.
MLA Analouei Adegani, Ebrahim et al. “Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination”. Gazi University Journal of Science, vol. 32, no. 2, 2019, pp. 637-4.
Vancouver Analouei Adegani E, Zıreh A, Jafarı M. Faber Polynomial Coefficient Estimates for Analytic Bi-Close-to-Convex Functions Defined by Subordination. Gazi University Journal of Science. 2019;32(2):637-4.