beta-bazilevič function

In this paper, we introduce a relatively new class, $mathcal{mathcal{b}}_{1}^beta(alpha)$, namely the class of beta-bazileviv{c} function is generated by the function bazileviv{c} $mathcal{b}_{1}(alpha)$. we introduce the class in question by constructing the alpha-convex function, $mathcal{m}(alpha)$, introduced by miller et al. cite{15}. 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 $f^{-1}$, the modulus of the logarithmic coefficients $log frac{f(z)}{z}$, the fekete-szeg{o} problem and the second hankel determinant problem.