Special Subfamilies of Holomorphic and Bi-univalent Functions related to Quasi-subordination
In the current work, special subfamilies of holomorphic bi-univalent functions based on quasi-subordination are introduced. Initial coefficient estimates for functions belonging to these subfamilies are established. Several consequences of our results and connections to known families are indicated.
Abdul Rahman S. Juma and Mohammed H. Saloomi, Generalized differential operator on bistarlike and biconvex functions associated by quasi-subordination, J. Phys.: Conf. Ser. 1003 (2018), 012046. https://doi.org/10.1088/1742-6596/1003/1/012046
R. M. Ali, S. K. Lee, V. Ravichandran and S. Subramaniam, Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions, Appl. Math. Lett. 25(3) (2012), 344-351. https://doi.org/10.1016/j.aml.2011.09.012
D. A. Brannan, J. Clunie and W. E. Kirwan, Coefficient estimates for a class of starlike functions, Canad. J. Math. 22 (1970), 476-485. https://doi.org/10.4153/CJM-1970-055-8
D. A. Brannan and T. S. Taha, On some classes of bi-univalent functions, Mathematical Analysis and Its Applications 3 (1985), 18-21.
E. Deniz, Certain subclasses of bi-univalent functions satisfying subordinate conditions, J. Class. Anal. 2(1) (2013), 49-60. https://doi.org/10.7153/jca-02-05
P. L. Duren, Univalent Functions, Springer-Verlag, New York, 1983.
S. P. Goyal and Rakesh Kumar, Coefficient estimates and quasi-subordination properties associated with certain subclasses of analytic and bi-univalent functions, Math. Slovaca 65(3) (2015), 533-544. https://doi.org/10.1515/ms-2015-0038
S. P. Goyal, O. Singh and R. Mukherjee, Certain results on a subclass of analytic and bi-univalent functions associated with coefficient estimates and quasi-subordination, Palestine Journal of Mathematics 5(1) (2016), 79-85.
M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1
N. Magesh, V. K. Balaji and J. Yamini, Certain subclasses of bistarlike and biconvex functions based on quasi-subordination, Abstract and Applied Analysis 2016 (2016), Article ID 3102960, 6 pp. https://doi.org/10.1155/2016/3102960
M. H. Mohd and M. Darus, Fekete-Szego problems for quasi-subordination classes, Abstract and Applied Analysis 2012 (2012), Article ID 192956, 14 pp. https://doi.org/10.1155/2012/192956
Z. Peng, G. Murugusundaramoorthy and T. Janani, Coefficient estimate of bi-univalent functions of complex order associated with the Hohlov operator, Journal of Complex Analysis 2014 (2014), Article ID 693908, 6 pp. https://doi.org/10.1155/2014/693908
Ch. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Gottingen, 1975.
F. Y. Ren, S. Owa and S. Fukui, Some inequalities on quasi-subordinate functions, Bull. Aust. Math. Soc. 43(2) (1991), 317-324. https://doi.org/10.1017/S0004972700029117
M. S. Robertson, Quasi-subordination and coefficient conjecture, Bull. Amer. Math. Soc. 76 (1970), 1-9. https://doi.org/10.1090/S0002-9904-1970-12356-4
Shashi Kant, Coefficients estimate for certain subclass of bi-univalent functions associated with quasi-subordination, J. Fract. Calc. Appl. 9(1) (2018), 195-203.
H. M. Srivastava, A. K. Mishra and P. Gochhayat, Certain subclasses analytic and bi-univalent functions, Appl. Math. Lett. 23(10) (2010), 1188-1192. https://doi.org/10.1016/j.aml.2010.05.009
S. R. Swamy, Ruscheweyh derivative and a new generalized Multiplier differential operator, Annals of Pure and Applied Mathematics 10(2) (2015), 229-238.
S. R. Swamy and Y. Sailaja, Fekete-Szegö inequality and quasi-subordination, Palestine Journal of Mathematics 10(2) (2021), in press.
S. R. Swamy and Y Sailaja, Horadam polynomial coefficient estimates for two families of holomorphic and bi-univalent functions, International Journal of Mathematics Trends and Technology 66(8) (2020), 131-138. https://doi.org/10.14445/22315373/IJMTT-V66I8P514
S. R. Swamy and Y. Sailaja, Sharp bounds of Fekete-Szego functional for quasi-subordination class, International Journal of Mathematics Trends and Technology 66(11) (2020), 87-94. https://doi.org/10.2478/ausm-2019-0008
H. Tang, G. Deng and S. Li, Coefficient estimates for new subclasses of Ma-Minda bi-univalent functions, J. Inequal. Appl. 2013 (2013), Article No. 317, 10 pp. https://doi.org/10.1186/1029-242X-2013-317
P. P. Vyas and S. Kant, Coefficients estimate for new subclass of bi-univalent functions associated with quasi-subordination, AIP Conference Proceedings 1953 (2018), 140068. https://doi.org/10.1063/1.5033243
P. P. Vyas and S. Kant, Certain subclasses of bi-univalent functions associated with quasi-subordination, Journal of Rajasthan Academy of Physical Sciences 15(4) (2016), 315-325.
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