Research Article
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Year 2018, , 70 - 76, 27.04.2018
https://doi.org/10.36753/mathenot.421763

Abstract

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.
  • [13] Pommerenke, C. H. , Univalent Functions, Vandenhoeck and Rupercht, Gottingen, (1975).
  • [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.
  • [22] Srivastava, H. M. and Owa, S., Current Topics In Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992.

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

Year 2018, , 70 - 76, 27.04.2018
https://doi.org/10.36753/mathenot.421763

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].

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.
  • [13] Pommerenke, C. H. , Univalent Functions, Vandenhoeck and Rupercht, Gottingen, (1975).
  • [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.
  • [22] Srivastava, H. M. and Owa, S., Current Topics In Analytic Function Theory, World Scientific Publishing Company, Singapore, New Jersey, London and Hong Kong, 1992.
There are 22 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Arzu Akgül

Publication Date April 27, 2018
Submission Date March 3, 2017
Published in Issue Year 2018

Cite

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 Akgül A. Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Math. Sci. Appl. E-Notes. April 2018;6(1):70-76. doi:10.36753/mathenot.421763
Chicago Akgül, Arzu. “Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms”. Mathematical Sciences and Applications E-Notes 6, no. 1 (April 2018): 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 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, 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 2018), 70-76. https://doi.org/10.36753/mathenot.421763.
JAMA 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, 2018, pp. 70-76, doi:10.36753/mathenot.421763.
Vancouver Akgül A. Coefficient Estimates for Certain Subclass of Bi-Univalent Functions Obtained With Polylogarithms. Math. Sci. Appl. E-Notes. 2018;6(1):70-6.

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