Convolutions of planar harmonic strip mappings. Issue 11 (2nd November 2021) - Dorff, Michael; Hamidi, Samaneh G.; Jahangiri, Jay M.; Yaar, Elif
Abstract : We consider classes of harmonic univalent functions f k = h k + g k ¯, ( k = 1, 2 ) that are shears of the analytic map h k − g k = 1 / 2 log ⁡ [ 1 + z / 1 − z ] with dilatation ω k = e i θ k z k . We prove that if the convolution f 1 ∗ f 2 is locally one-to-one and sense-preserving, then f 1 ∗ f 2 is convex in the direction of the real axis.