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 1/2 are also members of the family $\mathcal{B}(\mu, \beta, \lambda, \theta)$, for $0\leq \mu\leq 1$, $0\leq \beta < 1$, $\lambda\geq 0$ and $|\theta| < \frac{\pi}{2} $. 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.