Volume 15, Issue 2 (10-2020)                   IJMSI 2020, 15(2): 51-60 | Back to browse issues page

XML Print


Download citation:
BibTeX | RIS | EndNote | Medlars | ProCite | Reference Manager | RefWorks
Send citation to:

K. Wanas A, H. Majeed A. On Subclasses of Analytic and m-Fold Symmetric Bi-Univalent Functions. IJMSI. 2020; 15 (2) :51-60
URL: http://ijmsi.ir/article-1-1133-en.html
Abstract:  
The purpose of the present paper is to introduce and investigate two new subclasses π’¦π›΄π‘š(πœ†,𝛾;𝛼) and 𝒦∗π›΄π‘š(πœ†,𝛾;𝛽) of π›΄π‘š consisting of analytic and π‘š-fold symmetric bi-univalent functions defined in the open unit disk π‘ˆ. We obtain upper bounds for the coefficients |π‘Žπ‘š+1| and |π‘Žπ‘š| for functions belonging to these subclasses. Many of the well-known and new results are shown to follow as special cases of our results.
Type of Study: Research paper | Subject: Special

References
1. [1] S. Altinkaya and S. Yalçin, Coefficient bounds for certain subclasses of m-fold symmetric bi-univalent functions, Journal of Mathematics, Art. ID 241683, (2015), 1-5.
2. [2] S. Altinkaya and S. Yalçin, On some subclasses of m-fold symmetric bi-univalent functions, Commun. Fac. Sci. Univ. Ank. Series A1, 67(1)(2018), 29-36.
3. [3] D. A. Brannan and T. S. Taha, On Some classes of bi-univalent functions, Studia Univ. BabeΒΈs-Bolyai Math., 31(2)(1986), 70–77.
4. [4] P. L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer Verlag, New York, Berlin, Heidelberg and Tokyo, 1983.
5. [5] S. S. Eker, Coefficient bounds for subclasses of m-fold symmetric bi-univalent functions, Turk. J. Math., 40(2016), 641-646.
6. [6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24 (2011), 1569–1573.
7. [7] S. P. Goyal and P. Goswami, Estimate for initial Maclaurin coefficients of bi-univalent functions for a class defined by fractional derivatives, J. Egyptian Math. Soc., 20 (2012), 179-182.
8. [8] T. Hayami and S. Owa, Coefficient bounds for bi-univalent functions, Pan Amer. Math. J., 22(4)(2012), 15-26.
9. [9] W. Koepf, Coefficients of symmetric functions of bounded boundary rotations, Proc. Amer. Math. Soc., 105(1989), 324-329.
10. [10] N. Magesh and J. Yamini, Coefficient bounds for certain subclasses of bi-univalent functions, Int. Math. Forum, 8(27)(2013), 1337-1344.
11. [11] G. Murugusundaramoorthy, N. Magesh and V. Prameela, Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., Art. ID 573017, (2013), 1-3.
12. [12] C. Pommerenke, On the coefficients of close-to-convex functions, Michigan Math. J., 9(1962), 259-269.
13. [13] S. Prema and B. S. Keerthi, Coefficient bounds for certain subclasses of analytic function, J. Math. Anal., 4(1)(2013), 22-27.
14. [14] H. M. Srivastava and D. Bansal, Coefficient estimates for a subclass of analytic and bi-univalent functions, J. Egyptian Math. Soc., 23(2015), 242–246.
15. [15] H. M. Srivastava, S. Bulut, M. Caglar and N. Yagmur, Coefficient estimates for a general subclass of analytic and bi-univalent functions, Filomat, 27(5)(2013), 831–842.
16. [16] H. M. Srivastava, S. Gaboury and F. Ghanim, Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Universitatis Apulensis, 41(2015), 153–164.
17. [17] H. M. Srivastava, S. Gaboury and F. Ghanim, Initial coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions, Acta Mathematica Scientia, 36B(3)(2016), 863–871.
18. [18] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.
19. [19] 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(2)(2014), 1-10.
20. [20] H. Tang, H. M. Srivastava, S. Sivasubramanian and P. Gurusamy, The Fekete-Szego functional problems for some subclasses of m-fold symmetric bi-univalent functions, J. Math. Ineq., 10(2016), 1063-1092.
21. [21] Q.-H. Xu, Y.-C. Gui and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett., 25(2012), 990–994.
22. [22] Q.-H. Xu, H.-G. Xiao and H. M. Srivastava, A certain general subclass of analytic and bi-univalent functions and associated coefficient estimate problems, Appl. Math. Comput., 218(2012), 11461–11465.

Add your comments about this article : Your username or Email:
CAPTCHA

Β© 2020 All Rights Reserved | Iranian Journal of Mathematical Sciences and Informatics

Designed & Developed by : Yektaweb