On analytic functions of bounded boundary rotation of complex order

The class Vm(b,δ)Vm(b,δ) of locally univalent functions ff satisfying ∫02π|Re[1+1bzf′′(z)f′(z)]−δ(1−δ)|dθ≤mπ, where m≥2,δ∈[0,1) and b≠0b≠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 Vm(b,δ)Vm(b,δ) under certain integral operators and also deal with some radii problems.