Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms

Arzu Akgül

doi:10.36753/mathenot.421763

EN

Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms

Abstract

In the present work, the author determine coefficient bounds for functions in certain subclasses of analytic and bi-univalent functions. Several corollaries and consequences of the main results are also considered. The results, which are presented in this paper, generalize the recent work of Srivastava et al. [21].

Keywords

Analytic function,Bi-univalent function,coefficient bounds,polylogarithm function

References

[1] Akgül, A., Finding Initial Coefficients For A Class Of Bi-Univalent Functions Given By Q-Derivative, In: AIP Conference Proceedings 2018 Jan 12 (Vol. 1926, No. 1, p. 020001). AIP Publishing.
[2] Akgül, A. and Altınkaya, S., Coefficient Estimates Associated With A New Subclass Of Bi-Univalent Functions. Acta Universitatis Apulensis,52 (2017), 121-128.
[3] Akgül, A., New Subclasses of Analytic and Bi-Univalent Functions Involving a New Integral Operator Defined by Polylogarithm Function, Theory and Applications of Mathematics & Computer Science, 7 (2) (2017), 31 – 40.
[4] Altınkaya, ¸S. and Yalçın, S., Coefficient Estimates For Two New Subclass Of Bi-Univalent Functions With Respect To Symmetric Points, Journal of Function Spaces. Article ID 145242,(2015), 5 pages.
[5] Brannan, D. A. and Clunie, J. G., Aspects Of Contemporary Complex Analysis, in Proceeding of the NATO Advanced Study Instutte Held at University of Durham: July 1-20 , (1979), Academic Press, New York, N, YSA, 1980.
[6] Çağlar, M., Orhan, H., and Ya ˘gmur, N., Coefficient Bounds For New Subclass Of Bi-Univalent Functions, Filomat, 27 (2013),1165-1171.
[7] Crisan, O., Coefficient Estimates Of Certain Subclass Of Bi-Univalent Functions, Gen. Math. Notes, 16 (2013) no.2, 93-102.
[8] Duren, P. L., Grundlehren der Mathematischen Wissenchaften, Springer, New York, NY, USA,(1983).
[9] Frasin, B. A. and Aouf, M. K., New Subclass Of Bi-Univalent Functions, Appl. Math. Lett., 24 (2011), 1569-1573.
[10] Lewin, M., On A Coefficient Problem Of Bi-Univalent Functions, Proc. Amer. Math. Soc., 18 (1967), 63-68.

[11] Magesh, N. and Yamini, J., Coefficient Bounds For A Certain Subclass Of Bi-Univalent Functions, International Mathematical Forum 8(22),(2013), 1337-1344.
[12] Netanyahu, E., The Minimal Distance Of The Image Boundary From The Orijin And The Second Coefficient Of A Univalent Function in |z| < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
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[14] Ponnusamy, S. , Inclusion Theorems For Convolution Product Of Second Order Polylogariyhms And Functions With The Derivative In A Half Plane, Rocky Montain J. Math., 28(2) (1998), 695-733.
[15] Ponnusamy, S. and Sabapathy, S., Polylogarithms In The Theory Of Univalent Functions, Result in Mathematics, 30 (1996),136-150.
[16] Ruscheweyh, St., New Criteria For Univalent Functions, Proc. Amer. Math. Soc., 49 (1975),109-115.
[17] Porwal, S. and Darus, M., On A New Subclass Of Bi-Univalent Functions, J. Egypt. Math. Soc.,21(13),(2013),190- 193.
[18] G.Sâlâgean, Subclasses Of Univalent Functions, Lecture Notes In Math., Springer Verlag, 1013 (1983),362-372.
[19] Sakar, F. M. and Güney, H. Ö., Coefficient Bounds For A New Subclass Of Analytic Bi-Close-To-Convex Functions By Making Use Of Faber Polynomial Expansion. Turkish Journal of Mathematics, 41(4),(2017), 888-895.
[20] Shaqsi K. Al and Darus, M., An Oparator Defined By Convolution Involving The Polylogarithms Functions, Journal of Mathematics and Statics, 4 (2008), 1, 46-50.
[21] Srivastava, H. M., Mishra, A. K. and Gochhayat, P., Certain Subclass Of Analytic And Bi-Univalent Functions, Appl. Math. Lett.,23 (2010), 1188-1192.
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Details

Primary Language

English

Subjects

-

Journal Section

Research Article

Authors

Arzu Akgül

Publication Date

April 27, 2018

Submission Date

March 3, 2017

Acceptance Date

-

Published in Issue

Year 2018 Volume: 6 Number: 1

DOI

https://doi.org/10.36753/mathenot.421763

IZ

https://izlik.org/JA52ZZ68RZ

APA

Akgül, A. (2018). Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Mathematical Sciences and Applications E-Notes, 6(1), 70-76. https://doi.org/10.36753/mathenot.421763

AMA

1.Akgül A. Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Math. Sci. Appl. E-Notes. 2018;6(1):70-76. doi:10.36753/mathenot.421763

Chicago

Akgül, Arzu. 2018. “Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms”. Mathematical Sciences and Applications E-Notes 6 (1): 70-76. https://doi.org/10.36753/mathenot.421763.

EndNote

Akgül A (April 1, 2018) Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Mathematical Sciences and Applications E-Notes 6 1 70–76.

IEEE

[1]A. Akgül, “Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms”, Math. Sci. Appl. E-Notes, vol. 6, no. 1, pp. 70–76, Apr. 2018, doi: 10.36753/mathenot.421763.

ISNAD

Akgül, Arzu. “Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms”. Mathematical Sciences and Applications E-Notes 6/1 (April 1, 2018): 70-76. https://doi.org/10.36753/mathenot.421763.

JAMA

1.Akgül A. Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Math. Sci. Appl. E-Notes. 2018;6:70–76.

MLA

Akgül, Arzu. “Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms”. Mathematical Sciences and Applications E-Notes, vol. 6, no. 1, Apr. 2018, pp. 70-76, doi:10.36753/mathenot.421763.

Vancouver

1.Arzu Akgül. Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Math. Sci. Appl. E-Notes. 2018 Apr. 1;6(1):70-6. doi:10.36753/mathenot.421763

Cited By

Coefficient estimates for a general subclass of $m$-fold symmetric bi-univalent functions

Tbilisi Mathematical Journal

https://doi.org/10.32513/tbilisi/1561082575

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