Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2019, Cilt: 48 Sayı: 2, 365 - 371, 01.04.2019
https://doi.org/10.15672/hujms.545237

Öz

Kaynakça

  • 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

Yıl 2019, Cilt: 48 Sayı: 2, 365 - 371, 01.04.2019
https://doi.org/10.15672/hujms.545237

Öz

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.

Kaynakça

  • 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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Matematik
Yazarlar

Ebrahim A. Adegani 0000-0001-9176-3932

Samaneh G. Hamidi 0000-0002-5995-8892

Jay M. Jahangiri 0000-0002-5231-3530

Ahmad Zireh 0000-0002-3405-853X

Yayımlanma Tarihi 1 Nisan 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 48 Sayı: 2

Kaynak Göster

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. https://doi.org/10.15672/hujms.545237
AMA Adegani EA, Hamidi SG, Jahangiri JM, Zireh A. Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics. Nisan 2019;48(2):365-371. doi:10.15672/hujms.545237
Chicago Adegani, Ebrahim A., Samaneh G. Hamidi, Jay M. Jahangiri, ve Ahmad Zireh. “Coefficient Estimates for $m$-Fold Symmetric Bi-Subordinate Functions”. Hacettepe Journal of Mathematics and Statistics 48, sy. 2 (Nisan 2019): 365-71. https://doi.org/10.15672/hujms.545237.
EndNote Adegani EA, Hamidi SG, Jahangiri JM, Zireh A (01 Nisan 2019) Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics 48 2 365–371.
IEEE E. A. Adegani, S. G. Hamidi, J. M. Jahangiri, ve A. Zireh, “Coefficient estimates for $m$-fold symmetric bi-subordinate functions”, Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, ss. 365–371, 2019, doi: 10.15672/hujms.545237.
ISNAD Adegani, Ebrahim A. vd. “Coefficient Estimates for $m$-Fold Symmetric Bi-Subordinate Functions”. Hacettepe Journal of Mathematics and Statistics 48/2 (Nisan 2019), 365-371. https://doi.org/10.15672/hujms.545237.
JAMA Adegani EA, Hamidi SG, Jahangiri JM, Zireh A. Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics. 2019;48:365–371.
MLA Adegani, Ebrahim A. vd. “Coefficient Estimates for $m$-Fold Symmetric Bi-Subordinate Functions”. Hacettepe Journal of Mathematics and Statistics, c. 48, sy. 2, 2019, ss. 365-71, doi:10.15672/hujms.545237.
Vancouver Adegani EA, Hamidi SG, Jahangiri JM, Zireh A. Coefficient estimates for $m$-fold symmetric bi-subordinate functions. Hacettepe Journal of Mathematics and Statistics. 2019;48(2):365-71.