Bounded starlike functions of complex order

LetF(b, M) (b ≠ 0 complex,M>1/2) denote the class of functionsf(z) =z + Σ _n=2 ^∞ a _n z ⁿ analytic in U={z:|z|<1} which satisfy for fixedM, f(z)/z ≠ 0 inU and (left| {frac{{b - 1 + left[ {zf'{{left( z right)} mathord{left/ {vphantom {{left( z right)} {fleft( z right)}}} right. kern-0em} {fleft( z right)}}} right]}}{b} - M} right|< M, z in U) . In this note we obtain various representations for functions inF(b, M). We maximize |a₃=μa ₂ ² | over the classF(b, M). Also sharp coefficient bounds are established for functions inF(b, M). We also obtain the sharp radius of starlikeness of the classF(b, M).