Bi-Bazilevič functions of complex order involving Ruscheweyh type q-difference operator

Murugusundaramoorthy, Gangadharan; Bulut, Serap

doi:10.2478/aupcsm-2018-0001

Abstract

In this paper, we define a new subclass of bi-univalent functions involving q-difference operator in the open unit disk. For functions belonging to this class, we obtain estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3|.

References

[1] Ali, Rosihan M. et all. “Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions.” Appl. Math. Lett. 25, no. 3 (2012): 344–351. Cited on 8.10.1016/j.aml.2011.09.012
Search in Google Scholar Back to article
[2] Brannan, David A., and James Clunie, and William E. Kirwan. “Coefficient estimates for a class of star-like functions.” Canad. J. Math. 22 (1970): 476–485. Cited on 8.10.4153/CJM-1970-055-8
Search in Google Scholar Back to article
[3] Aspects of Contemporary Complex Analysis. Edited by David A. Brannan and James G. Clunie. London: Academic Press, 1980. Cited on 8.
Search in Google Scholar Back to article
[4] Brannan, David A., and T.S. Taha. “On some classes of bi-univalent functions.” Studia Univ. Babeş-Bolyai Math. 31, no. 2 (1986): 70–77. Cited on 8.
Search in Google Scholar Back to article
[5] Bulut, Serap. “Certain subclasses of analytic and bi-univalent functions involving the q-derivative operator.” Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 66, no. 1 (2017): 108–114. Cited on 8.10.1501/Commua1_0000000780
Search in Google Scholar Back to article
[6] Deniz, Erhan. “Certain subclasses of bi-univalent functions satisfying subordinate conditions.” J. Class. Anal. 2, no. 1 (2013): 49–60. Cited on 8.10.7153/jca-02-05
Search in Google Scholar Back to article
[7] Frasin, Basem A., and Mohamed K. Aouf. “New subclasses of bi-univalent functions.” Appl. Math. Lett. 24, no. 9 (2011): 1569–1573. Cited on 8.10.1016/j.aml.2011.03.048
Search in Google Scholar Back to article
[8] Jackson, F.H. “On q-functions and a certain difference operator.” Trans. Royal Soc. Edinburgh 46, no. 2 (1909): 253–281. Cited on 6 and 7.10.1017/S0080456800002751
Search in Google Scholar Back to article
[9] Hayami, Toshio, and Shigeyoshi Owa. “Coefficient bounds for bi-univalent functions.” PanAmer. Math. J. 22, no. 4 (2012): 15–26. Cited on 8.
Search in Google Scholar Back to article
[10] Inayat Noor, Khalida. “On Bazilevic functions of complex order.” Nihonkai Math. J. 3, no. 2 (1992): 115–124. Cited on 8.
Search in Google Scholar Back to article
[11] Kanas, Stanisława, and Dorina Răducanu. “Some class of analytic functions related to conic domains.” Math. Slovaca 64, no. 5 (2014): 1183–1196. Cited on 6 and 7.10.2478/s12175-014-0268-9
Search in Google Scholar Back to article
[12] Lewin, Mordechai. “On a coefficient problem for bi-univalent functions.” Proc. Amer. Math. Soc. 18 (1967): 63–68. Cited on 8.10.1090/S0002-9939-1967-0206255-1
Search in Google Scholar Back to article
[13] Ma, Wan Cang, and David Minda. “A unified treatment of some special classes of univalent functions.” In Proceedings of the Conference on Complex Analysis (Tianjin, 1992), 157–169. Vol I of Conf. Proc. Lecture Notes Anal. Cambridge, MA: Int. Press, 1994. Cited on 6.
Search in Google Scholar Back to article
[14] Netanyahu, Elisha. “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. Cited on 8.10.1007/BF00247676
Search in Google Scholar Back to article
[15] Pommerenke, Christian. Univalent functions. Vol. 25 of Mathematische Lehrbücher. Göttingen: Vandenhoeck & Ruprecht, 1975. Cited on 10.
Search in Google Scholar Back to article
[16] Srivastava, H. M., and G. Murugusundaramoorthy, and K. Vijaya. “Coefficient estimates for some families of bi-Bazilevič functions of the Ma-Minda type involving the Hohlov operator.” J. Class. Anal. 2, no. 2, (2013): 167–181. Cited on 8.10.7153/jca-02-14
Search in Google Scholar Back to article
[17] Srivastava, Hari M., and Akshaya K. Mishra, and Priyabrat Gochhayat. “Certain subclasses of analytic and bi-univalent functions.” Appl. Math. Lett. 23, no. 10, (2010): 1188–1192. Cited on 8.10.1016/j.aml.2010.05.009
Search in Google Scholar Back to article
[18] Taha, T.S. Topics in Univalent Function Theory, Ph.D. Thesis. London: University of London, 1981. Cited on 8.
Search in Google Scholar Back to article

Bi-Bazilevič functions of complex order involving Ruscheweyh type q-difference operator

Abstract

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