STARLIKENESS ASSOCIATED WITH THE SINE HYPERBOLIC FUNCTION

【摘要】 Let q_λ(z)=1+λsinh(ζ),0 <λ <1/sinh(1) be a non-vanishing analytic function in the open unit disk.We introduce a subclass S~*(q_λ) of starlike functions which contains the functions f such that zf’/f is subordinated by q_λ.We establish inclusion and radii results for the class S~*(q_λ) for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S~*(q_λ).We also find a sharp bound for the third Hankel determinant for the case λ=1/2.更多还原

【Abstract】 Let q_λ(z)=1+λsinh(ζ),0 <λ <1/sinh(1) be a non-vanishing analytic function in the open unit disk.We introduce a subclass S~*(q_λ) of starlike functions which contains the functions f such that zf’/f is subordinated by q_λ.We establish inclusion and radii results for the class S~*(q_λ) for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S~*(q_λ).We also find a sharp bound for the third Hankel determinant for the case λ=1/2.更多还原