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Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator

Year 2019, Volume: 2 Issue: 1, 9 - 12, 30.10.2019

Fethiye Müge Sakar Seher Melike Aydoğan Şahsene Altınkaya

Abstract

In this study, we construct a new subclass of $m$-fold symmetric bi-univalent functions using by Hadamard product and generalized Salagean differential operator in the open unit disk $U=\left\{ z\in \mathbb{C} :\left\vert z\right\vert <1\right\} $. We establish upper bounds for the coefficients $\left\vert a_{m+1}\right\vert $ and $\left\vert a_{2m+1}\right\vert $ belonging to this new class. The results presented here generalize some of the earlier studies.

Keywords

Coefficient estimates bi-univalent functions m-fold symmetric functions

Supporting Institution

Batman University

Project Number

BTUBAP2018-IIBF-2

References

  • [1] F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 27 (2004), 1429-1436.
  • [2] D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babe¸s-Bolyai Mathematica, 31 (1986), 70-77.
  • [3] S. Bulut, Coefficient estimates for general subclasses ofm-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40 (2016), 1386-1397.
  • [4] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA 259, 1983.
  • [5] S. G. Hamidi, J. M. Jahangiri, Unpredictability of the coefficients ofm-fold symmetric bi-starlike functions, Internat. J. Math., 25 (2014), 1-8.
  • [6] M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18 (1967), 63-68.
  • [7] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
  • [8] Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975.
  • [9] G. S. Salagean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian Finish Seminar, Part 1 (Bucharest, 1981), 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983.
  • [10] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23 (2010), 1188-1192.
  • [11] H. M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefficient bounds for a subclass ofm-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7 (2014), 1-10.
  • [12] S. Sumer Eker, Coefficient bounds for subclasses ofm-fold symmetric bi-univalent functions, Turkish J. Math., 40 (2016), 641-646.

Year 2019, Volume: 2 Issue: 1, 9 - 12, 30.10.2019

Fethiye Müge Sakar Seher Melike Aydoğan Şahsene Altınkaya

Abstract

Project Number

BTUBAP2018-IIBF-2

References

  • [1] F. M. Al-Oboudi, On univalent functions defined by a generalized Salagean operator, Int. J. Math. Math. Sci., 27 (2004), 1429-1436.
  • [2] D. A. Brannan, T. S. Taha, On some classes of bi-univalent functions, Studia Universitatis Babe¸s-Bolyai Mathematica, 31 (1986), 70-77.
  • [3] S. Bulut, Coefficient estimates for general subclasses ofm-fold symmetric analytic bi-univalent functions, Turkish J. Math., 40 (2016), 1386-1397.
  • [4] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Springer, New York, USA 259, 1983.
  • [5] S. G. Hamidi, J. M. Jahangiri, Unpredictability of the coefficients ofm-fold symmetric bi-starlike functions, Internat. J. Math., 25 (2014), 1-8.
  • [6] M. Lewin, On a coefficient problem for bi-univalent functions, Proceedings of the American Mathematical Society, 18 (1967), 63-68.
  • [7] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in jzj < 1, Archive for Rational Mechanics and Analysis, 32 (1969), 100-112.
  • [8] Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975.
  • [9] G. S. Salagean, Subclasses of univalent functions, in Complex Analysis, Fifth Romanian Finish Seminar, Part 1 (Bucharest, 1981), 1013 of Lecture Notes in Mathematics, 362-372, Springer, Berlin, Germany, 1983.
  • [10] H. M. Srivastava, A. K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Applied Mathematics Letters, 23 (2010), 1188-1192.
  • [11] H. M. Srivastava, S. Sivasubramanian, R. Sivakumar, Initial coefficient bounds for a subclass ofm-fold symmetric bi-univalent functions, Tbilisi Mathematical Journal, 7 (2014), 1-10.
  • [12] S. Sumer Eker, Coefficient bounds for subclasses ofm-fold symmetric bi-univalent functions, Turkish J. Math., 40 (2016), 641-646.
There are 12 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Fethiye Müge Sakar 0000-0002-3884-3957

Seher Melike Aydoğan This is me 0000-0002-4822-9571

Şahsene Altınkaya 0000-0002-7950-8450

Project Number BTUBAP2018-IIBF-2
Publication Date October 30, 2019
Acceptance Date September 12, 2019
Published in Issue Year 2019 Volume: 2 Issue: 1

Cite

APA Sakar, F. M., Aydoğan, S. M., & Altınkaya, Ş. (2019). Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology, 2(1), 9-12.
AMA Sakar FM, Aydoğan SM, Altınkaya Ş. Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology. October 2019;2(1):9-12.
Chicago Sakar, Fethiye Müge, Seher Melike Aydoğan, and Şahsene Altınkaya. “Coefficient Bounds for a Subclass of $m$-Fold Symmetric Bi-Univalent Functions Involving Hadamard Product and Differential Operator”. Conference Proceedings of Science and Technology 2, no. 1 (October 2019): 9-12.
EndNote Sakar FM, Aydoğan SM, Altınkaya Ş (October 1, 2019) Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology 2 1 9–12.
IEEE F. M. Sakar, S. M. Aydoğan, and Ş. Altınkaya, “Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator”, Conference Proceedings of Science and Technology, vol. 2, no. 1, pp. 9–12, 2019.
ISNAD Sakar, Fethiye Müge et al. “Coefficient Bounds for a Subclass of $m$-Fold Symmetric Bi-Univalent Functions Involving Hadamard Product and Differential Operator”. Conference Proceedings of Science and Technology 2/1 (October 2019), 9-12.
JAMA Sakar FM, Aydoğan SM, Altınkaya Ş. Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology. 2019;2:9–12.
MLA Sakar, Fethiye Müge et al. “Coefficient Bounds for a Subclass of $m$-Fold Symmetric Bi-Univalent Functions Involving Hadamard Product and Differential Operator”. Conference Proceedings of Science and Technology, vol. 2, no. 1, 2019, pp. 9-12.
Vancouver Sakar FM, Aydoğan SM, Altınkaya Ş. Coefficient Bounds for a Subclass of $m$-fold Symmetric Bi-univalent Functions Involving Hadamard Product and Differential Operator. Conference Proceedings of Science and Technology. 2019;2(1):9-12.
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