Some properties of functions associated with close-to-convex and starlike of order αα

For analytic functions f(z)f(z) normalized with f(0)=0f(0)=0 and f′(0)=1f′(0)=1 in the open unit disk UU, a new class A(β1,β2;λ)A(β1,β2;λ) of f(z)f(z) satisfying some conditions with some complex numbers β1β1 and β2β2 is introduced. The object of the present paper is to discuss some properties for A(β1,β2;λ)A(β1,β2;λ) of f(z)f(z) associated with close-to-convex and starlike of order αα in UU.