For *k=1,2*, let *f_k=h_k+\overline{g_k}* be normalized harmonic right half-plane or vertical strip mappings. We consider the convex combination *\hat{f}=\eta f_1+(1-\eta)f_2 =\eta h_1+(1-\eta)h_2 +\overline{\overline{\eta} g_1+(1-\overline{\eta})g_2}* and the combination *\tilde{f}=\eta h_1+(1-\eta)h_2+\overline{\eta g_1+(1-\eta)g_2}*. For real *\eta*, the two mappings *\hat{f}* and *\tilde{f}* are the same. We investigate the univalence and directional convexity of... Show more

December 17, 2020

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Directional Convexity of Combinations of Harmonic Half-Plane and Strip Mappings

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