Year 2022,
Volume: 10 Issue: 2, 368 - 374, 31.10.2022
Mohamed Kamal Aouf
,
Tamer Seoudy
References
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- [4] M.K. Aouf and T.M. Seoudy, Certain class of bi–Bazilevic functions with bounded boundary rotation involving Salagean operator, Constructive Math.
Anal., 3(2020), no. 4, 139–149.
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Math. Soc., 20(2012), no.3, 179–182.
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- [14] R. Singh and V. Singh, On a class of bounded starlike functions, Indian J. Pure Appl. Math., 5 (1974), 733–754.
- [15] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.
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Classes of bi-Starlike and bi-Convex Bounded Functions with Complex Order
Year 2022,
Volume: 10 Issue: 2, 368 - 374, 31.10.2022
Mohamed Kamal Aouf
,
Tamer Seoudy
Abstract
In this paper, estimates for second and third coefficients of certain classes of bi-starlike and bi-convex bounded functions with complex order in the open unit disk are determined, and certain special cases are also indicated.
References
- [1] R. M. Ali, S. K. Lee, V. Ravichandran and S. Supramaniam, Coefficient estimates for bi-univalent Ma-Minda stalike and convex functions, Appl. Math.
Lett., 25(2012), no. 3, 344–351.
- [2] M. K. Aouf, Bounded spiral-like functions with fixed second coefficient, Internat. J. Math. Math. Sci., 12(1989), no. 1, 113-118.
- [3] M.K. Aouf, Bounded pvalent Robertson functions of order a, Indian J. Pure Appl. Math., 16 (2001), no. 7, 775–790.
- [4] M.K. Aouf and T.M. Seoudy, Certain class of bi–Bazilevic functions with bounded boundary rotation involving Salagean operator, Constructive Math.
Anal., 3(2020), no. 4, 139–149.
- [5] D. A. Brannan and T.S. Taha, D.A.Brannan,T.S.Taha,On some classes of bi-univalent functions, Studia Univ. Babe¸s-Bolyai Math.,31(1986), no. 2,
70–77.
- [6] B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), no. 9, 1569–1573.
- [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), no.3, 179–182.
- [8] P. K. Kulshrestha, Bounded Rebertson functions, Rend. Mat., 6 (1976), no. 7, 137–150.
- [9] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63–68.
- [10] R. J. Libera and A. E. Livingston, Bounded functions with postive real part, Czechoslovak Math. J., 22(1972), no. 97, 195-209.
- [11] A. M. Nasr and M. K. Aouf, Bounded convex functions of complex order, Mansoura Sci. Bull., 10 (1983), 513–526.
- [12] A. M. Nasr and M. K. Aouf, Bounded starlike functions of complex order, Proc. Indian Acad. Sci. (Math. Sci.), 92 (1983), no. 2, 97–102.
- [13] M. S. Robertson, On the theory of univalent functions, Ann. Math., 37 (1936), 374–408.
- [14] R. Singh and V. Singh, On a class of bounded starlike functions, Indian J. Pure Appl. Math., 5 (1974), 733–754.
- [15] H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23(2010), 1188–1192.
- [16] T. S. Taha, Topics in univalent function theory, Ph. D. Thesis, University of London,1981.