Sa'adatul Fitri - Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, East Java ۶۵۱۴۵, Indonesia.
Mohamad Muslikh - Department of Mathematics, Faculty of Mathematics and Natural Sciences, University of Brawijaya, Malang, East Java ۶۵۱۴۵, Indonesia.

In this paper, we introduce a relatively new class, \mathcal{\mathcal{B}}_{۱}^\beta(\alpha), namely the class of Beta-Bazilevi\v{c} function is generated by the function Bazilevi\v{c} \mathcal{B}_{۱}(\alpha). We introduce the class in question by constructing the Alpha-Convex function, \mathcal{M}(\alpha), introduced by Miller et al. \cite{۱۵}. Using Lemmas of function with positive real part, we were given a sharp estimate of coefficient problems. The coefficient problems to be solved are the modulus of initial coefficients f, the modulus of inverse coefficients f^{-۱}, the modulus of the Logarithmic coefficients \log \frac{f(z)}{z}, the Fekete-Szeg\"{o} problem and the second Hankel determinant problem.

Bazilevic function, Alpha-Convex function, Function with positive real part, Coefficient