Subordination of functions in subclass of Bazilevič Functions B 1(α, β)

Let f be analytic in the unit disc D = { z : | z | < 1} with f ( z ) = z + ∑ n = 2 ∞ a n z n , and for α ≥ 0 and 0 < β ≤ 1, let B 1 ( α, ß ), denote for the class of Bazilevič functions satisfying the expression | arg z 1 − α f ′ ( z ) f ( z ) 1 − α | < β π 2 . We give sharp estimates for various coefficient problems for functions in B 1 ( α, β ), which unify and extend well-known results for starlike functions, strongly starlike functions and functions whose derivative has positive real part in domain D .