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Journals / Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics / 2019 / Volume: 68 Issue: 2

Coefficient bounds for a certain subclass of analytic and bi-univalent functions

Nizami Mustafa0000-0001-9640-8526
Veysel Nezir0000-0002-2758-0274
Pages
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Publication Date
2019-08-01
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Some interesting corollaries and applications of the results obtained here are also discussed.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we introduce and investigate a new subclass of the a-nalytic and bi-univalent functions in the open unit disk in the complex plane.
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Key Findings & Data:For the functions belonging to this class, we obtain estimates on the first three coefficients in their Taylor-Maclaurin series expansion.
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Conclusion & Impact:Some interesting corollaries and applications of the results obtained here are also discussed.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Univalent functions · analytic functions · bi-univalent functions

Abstract

In this paper, we introduce and investigate a new subclass of the a-nalytic and bi-univalent functions in the open unit disk in the complex plane. For the functions belonging to this class, we obtain estimates on the first three coefficients in their Taylor-Maclaurin series expansion. Some interesting corollaries and applications of the results obtained here are also discussed.

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Cite This Article

Mustafa, N., Nezir, V. (2019). Coefficient bounds for a certain subclass of analytic and bi-univalent functions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Volume: 68 Issue: 2. https://doi.org/10.31801/cfsuasmas.540642

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References (31)

  1. Ali R. M., Lee S. K., Ravichandran V. and Supramanian S., Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25(3), (2012), 334--351.
  2. Brannan D. A. and Clunie J. G., Aspects of Contemporary Complex Analysis, Proceeding of the NATO Advanced Study Institute held at the University of Durham, Durham; July 1-20, 1979, (Academic Press, New York and London, 1980).
  3. Brannan D. A. and Taha T. S., On some classes of bi-univalent functions, Mathematical Analysis and Its Applications 3, (1985), 18-21.
  4. Bulut S., Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Mat. 43(2), 59--65, 2013.
  5. Çağlar M., Orhan H. and Yağmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat 27(7), 1165--1171, 2013.
  6. Deniz E., Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Classical Anal. 2(1), (2013), 49--60.
  7. Frasin B. A. and Aouf M. K., New subclasses of bi-univalent functions, Appl. Math. Lett. 24(9), (2011), 1569--1573.
  8. Goyal S. P. and Goswami P., Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc. 20, (2012), 179--182.
  9. Hayami T. and Owa S., Coefficient bounds for bi-univalent functions, Pan Amer. Math. J. 22(4), 15-26, 2012.
  10. Kim Y. C. and Srivastava H. M., Some subordination properties for spirallike functions, Appl. Math. Comput. 203(2), (2008), 838--842.
  11. Lewin M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18, (1967), 63--68.
  12. Ma W. C. and Minda D., A unified treatment of some special classes of functions, in: Proceedings of the Conference on Complex Analysis, Tianjin,, (1992),157-169, Conf. Proc. Lecture Notes anal. I, Int. Press, Cambridge, MA, 1994.
  13. Magesh N. and Yamini J., Coeffcient bounds for certain subclasses of bi-univalent functions, Internat. Math. Forum 8(27), (2013), 1337--1344.
  14. Miller S. S. and Mocanu P. T., Differential subordinations, Monographs and Textbooks in Pure and Applied Mathematics 225, Dekker, New York, 2000.
  15. Murugusundaramoorthy G., Magesh N. and Prameela V., Coefficient bounds for certain subclasses of bi-univalent functions, Abs. Appl. Anal., (2013), Article Id 573017, 3 pages.
  16. Netanyahu E., The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z|<1, Arch. Rational Mech. Anal. 32, (1969), 100--112.
  17. Orhan H., Magesh N. and Balaji V. K., Initial Coefficient Bounds for a General Class of Bi-Univalent Functions, Filomat 29(6), (2015), 1259--1267.
  18. Pommerenke C., Univalent Functions, Vandenhoeck and Rupercht, Göttingen, 1975.
  19. Prema S. and Keerthi B. S., Coefficient bounds for certain subclasses of analytic functions, J. Math. Anal. 4(1), (2013), 22-27.
  20. Ravichandran V., Polatoglu Y., Bolcal M. and Sen A., Certain subclasses of starlike and convex functions of complex order, Hacettepe J. Math. Stat. 34, (2005), 9--15.
  21. Sivaprasad Kumar S., Kumar V. and Ravichandran V., Estimates for the initial coefficients of bi-univalent functions, (2012), arXiv:1203.5480v1.
  22. Srivastava H. M., Mishra A. K. and Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23, (2010), 1188--1192.
  23. Srivastava H. M., Some inequalities and other results associated with certain subclasses of univalent and bi-univalent analytic functions, in Nonlinear Analysis: Stability; Approximation; and Inequalities (Panos M. Pardalos, Pando G. Georgiev, and Hari M. Srivastava, Editors), Springer Series on Optimization and Its Applications Vol. 68, Springer-Verlag, Berlin, Heidelberg and New York, (2012), 607--630.
  24. Srivastava H. M., Bulut S., Çağlar M. and Yağmur N., Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat 27(5), (2013), 831--842.
  25. Srivastava H. M., Murugusundaramoorthy G. and Magesh N., On certain subclasses of bi-univalent functions associated with Hohlov operator, Global J. Math. Anal. 1(2), (2013), 67--73.
  26. Srivastava H. M., Xu Q. H. and Wu G. P., Coefficient estimates for certain subclasses of spiral-like functions of complex order, Appl. Math. Lett. 23(7), (2010), 763--768.
  27. Xu Q. H., Gui Y. C. and Srivastava H. M., Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25(6), (2012), 990-994.
  28. Xu Q. H., Xiao H. G. and Srivastava H. M., A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput. 218(23), (2012), 11461--11465.
  29. Xu Q. H., Cai Q. M. and Srivastava H. M., Sharp coefficient estimates for certain subclasses of starlike functions of complex order, Appl. Math. Comput. 225, (2013), 43--49.
  30. Bulut S., Coefficient estimates for a class of analytic and bi-univalent functions, Novi Sad J. Mat. 43(2), 59--65, 2013.
  31. Ma W. C. and Minda D., A unified treatment of some special classes of functions, in: Proceedings of the Conference on Complex Analysis, Tianjin,, (1992),157-169, Conf. Proc. Lecture Notes anal. I, Int. Press, Cambridge, MA, 1994.