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Year 2019, Volume 48, Issue 2, 365 - 371, 01.04.2019
https://doi.org/10.15672/hujms.545237

Abstract

References

  • H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 130, 179-222, 2006.
  • H. Airault and J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126, 343-367, 2002.
  • P.L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, NY, 1983.
  • B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569-1573, 2011.
  • S.G. Hamidi and J.M. Jahangiri Unpredictability of the coefficients of m-fold symmetric bi-starlike functions, Internat. J. Math. 25, 8 pp, 2014.
  • S.G. Hamidi and J.M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris. 354, 365-370, 2016.
  • J.M. Jahangiri and S.G. Hamidi, Coefficient estimates for certain classes of biunivalent functions, Int. J. Math. Math. Sci. Article ID: 190560, 1-4, 2013.
  • W.C. Ma and D.A. Minda, Unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Int Press, 157- 169, 1994.
  • H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23, 1188-1192, 2010.
  • H.M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi. Math. J. 7, 1-10, 2014.
  • S. Sümer Eker, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turk. J. Math. 1, 1-6, 2015.
  • P.G. Todorov, On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl. 162, 268-276, 1991.

Coefficient estimates for $m$-fold symmetric bi-subordinate functions

Year 2019, Volume 48, Issue 2, 365 - 371, 01.04.2019
https://doi.org/10.15672/hujms.545237

Abstract

A function is said to be bi-univalent in the open unit disk $\mathbb{U}$ if both the function and its inverse map are univalent in $\mathbb{U}$. By the same token, a function is said to be bi-subordinate in $\mathbb{U}$ if both the function and its inverse map are subordinate to a given function in $\mathbb{U}$. In this paper, we consider the m-fold symmtric transform of such functions and use their Faber polynomial expansions to find upper bounds for their n-th ($n\geq 3$) coefficients subject to a given gap series condition. We also determine bounds for the first two coefficients of such functions with no restrictions imposed.

References

  • H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 130, 179-222, 2006.
  • H. Airault and J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126, 343-367, 2002.
  • P.L. Duren, Univalent Functions, in: Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, NY, 1983.
  • B.A. Frasin and M.K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24, 1569-1573, 2011.
  • S.G. Hamidi and J.M. Jahangiri Unpredictability of the coefficients of m-fold symmetric bi-starlike functions, Internat. J. Math. 25, 8 pp, 2014.
  • S.G. Hamidi and J.M. Jahangiri, Faber polynomial coefficients of bi-subordinate functions, C. R. Acad. Sci. Paris. 354, 365-370, 2016.
  • J.M. Jahangiri and S.G. Hamidi, Coefficient estimates for certain classes of biunivalent functions, Int. J. Math. Math. Sci. Article ID: 190560, 1-4, 2013.
  • W.C. Ma and D.A. Minda, Unified treatment of some special classes of univalent functions, in: Proceedings of the Conference on Complex Analysis, Int Press, 157- 169, 1994.
  • H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and biunivalent functions, Appl. Math. Lett. 23, 1188-1192, 2010.
  • H.M. Srivastava, S. Sivasubramanian and R. Sivakumar, Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions, Tbilisi. Math. J. 7, 1-10, 2014.
  • S. Sümer Eker, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turk. J. Math. 1, 1-6, 2015.
  • P.G. Todorov, On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl. 162, 268-276, 1991.

Details

Primary Language English
Subjects Mathematics
Journal Section Mathematics
Authors

Ebrahim A. ADEGANİ (Primary Author)
0000-0001-9176-3932


Samaneh G. HAMİDİ
0000-0002-5995-8892


Jay M. JAHANGİRİ
0000-0002-5231-3530


Ahmad ZİREH
0000-0002-3405-853X

Publication Date April 1, 2019
Published in Issue Year 2019, Volume 48, Issue 2

Cite

Bibtex @research article { hujms546366, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2019}, pages = {365 - 371}, doi = {10.15672/hujms.545237}, title = {Coefficient estimates for \$m\$-fold symmetric bi-subordinate functions}, key = {cite}, author = {Adegani, Ebrahim A. and Hamidi, Samaneh G. and Jahangiri, Jay M. and Zireh, Ahmad} }
APA Adegani, E. A. , Hamidi, S. G. , Jahangiri, J. M. & Zireh, A. (2019). Coefficient estimates for $m$-fold symmetric bi-subordinate functions . Hacettepe Journal of Mathematics and Statistics , 48 (2) , 365-371 . DOI: 10.15672/hujms.545237
MLA Adegani, E. A. , Hamidi, S. G. , Jahangiri, J. M. , Zireh, A. "Coefficient estimates for $m$-fold symmetric bi-subordinate functions" . Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 365-371 <https://dergipark.org.tr/en/pub/hujms/article/546366>
Chicago Adegani, E. A. , Hamidi, S. G. , Jahangiri, J. M. , Zireh, A. "Coefficient estimates for $m$-fold symmetric bi-subordinate functions". Hacettepe Journal of Mathematics and Statistics 48 (2019 ): 365-371
RIS TY - JOUR T1 - Coefficient estimates for $m$-fold symmetric bi-subordinate functions AU - Ebrahim A. Adegani , Samaneh G. Hamidi , Jay M. Jahangiri , Ahmad Zireh Y1 - 2019 PY - 2019 N1 - doi: 10.15672/hujms.545237 DO - 10.15672/hujms.545237 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 365 EP - 371 VL - 48 IS - 2 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.545237 UR - https://doi.org/10.15672/hujms.545237 Y2 - 2016 ER -
EndNote %0 Hacettepe Journal of Mathematics and Statistics Coefficient estimates for $m$-fold symmetric bi-subordinate functions %A Ebrahim A. Adegani , Samaneh G. Hamidi , Jay M. Jahangiri , Ahmad Zireh %T Coefficient estimates for $m$-fold symmetric bi-subordinate functions %D 2019 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 48 %N 2 %R doi: 10.15672/hujms.545237 %U 10.15672/hujms.545237
ISNAD Adegani, Ebrahim A. , Hamidi, Samaneh G. , Jahangiri, Jay M. , Zireh, Ahmad . "Coefficient estimates for $m$-fold symmetric bi-subordinate functions". Hacettepe Journal of Mathematics and Statistics 48 / 2 (April 2019): 365-371 . https://doi.org/10.15672/hujms.545237
AMA Adegani E. A. , Hamidi S. G. , Jahangiri J. M. , Zireh A. Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 365-371.
Vancouver Adegani E. A. , Hamidi S. G. , Jahangiri J. M. , Zireh A. Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics. 2019; 48(2): 365-371.
IEEE E. A. Adegani , S. G. Hamidi , J. M. Jahangiri and A. Zireh , "Coefficient estimates for $m$-fold symmetric bi-subordinate functions", Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 2, pp. 365-371, Apr. 2019, doi:10.15672/hujms.545237