Harmonic Functions Starlike in the Unit Disk

Complex-valued harmonic functions that are univalent and sense-preserving in the unit disk Δ can be written in the form f = h + ḡ, where h and g are analytic in Δ. We give univalence criteria and sufficient coefficient conditions for normalized harmonic functions that are starlike of order α, 0 ≤ α < 1. These coefficient conditions are also shown to be necessary when h has negative and g has positive coefficients. These lead to extreme points and distortion bounds.