Brief Study On A New Family of Analytic Functions

The authors introduced a new class of analytic functions in this study by means of convolution principle and obtain its relations with some well-known subclasses of analytic univalent functions in geometric functions theory in the open unit disk \mathbb{D}. Furthermore, as a special case, we show that convex functions of order ۱/۲ are also members of the family \mathcal{B}(\mu, \beta, \lambda, \theta), for ۰\leq \mu\leq ۱, ۰\leq \beta < ۱, \lambda\geq ۰ and |\theta| < \frac{\pi}{۲} . Thereafter, we obtain the bounds of the first three Taylorr- Maclaurin coefficients for functions f(z) belonging to the class \mathcal{B}(\mu, \alpha, \beta, \lambda, \theta; \check{p}) associated with shell-like curve.

Keywords:

Univalent , Analytic , Starlike , Convex , Spiralike , Bounded Turning