Rashidah Omar and Suzeini Abdul Halim and Aini Janteng
Subclasses of BiUnivalent Functions Associated with Hohlov Operator
465 - 468
2017
11
10
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/10008113
https://publications.waset.org/vol/130
World Academy of Science, Engineering and Technology
The coefficients estimate problem for TaylorMaclaurin series is still an open problem especially for a function in the subclass of biunivalent functions. A function f A is said to be biunivalent in the open unit disk D if both f and f1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) f&rsquo;(0) &ndash; 10. The class of biunivalent is denoted by The subordination concept is used in determining second and third TaylorMaclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of biunivalent functions which are subordinated to the function &phi;. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) 0 and w(z) &lt; 1 satisfying f(z) gw(z). In this paper, two subclasses of biunivalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.
Open Science Index 130, 2017