On Certain Generalized Bazilevic type Functions Associated with Conic Regions

Let f and g be analytic in the open unit disc and, for α, β ≥ 0, let J (α, β, f, g) = zf′ (z)/ f 1−α(z)g ^α(z) + β ( 1 + zf′′(z)/ f ′(z) ) − β (1 − α) zf′ (z) /f(z) − αβ zg′ (z)/ g(z) . The main aim of this paper is to study the class of analytic functions which map J (α, β, f, g) onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.