On analytic functions of bounded boundary rotation of complex order
The class V m ( b , δ ) of locally univalent functions f satisfying ∫ 0 2 π | Re [ 1 + 1 b z f ′ ′ ( z ) f ′ ( z ) ] − δ ( 1 − δ ) | d θ ≤ m π , where m ≥ 2 , δ ∈ [ 0 , 1 ) and b ≠ 0 (complex), is introduced. Some basic properties of this class such as distortion result, arc-length problem, and rate of growth of coefficients are studied. We also investigate the functions in V m ( b , δ ) under certain integral operators and also deal with some radii problems.