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 $0leq muleq 1$, $0leq beta < 1$, $lambdageq 0$ 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.