Abstract
In the article taking suitable harmonic map**s \(f_{1}, f_{2}\) and \(f_{3}, f_{4}\) such that their convolution \(F_{1}=f_{1}*f_{2}\) and \(F_{2}=f_{3}*f_{4}\) be also harmonic univalent map**s then we construct a new harmonic map** \(F_{3}=tF_{1}+(1-t)F_{2}=t(h_{1}*h_{2})+(1-t)(h_{3}*h_{4})+t(\overline{g_{1}*g_{2}})+(1-t)(\overline{g_{3}*g_{4}})=H_{3}+\overline{G_3}\) and prove that under certain condition \(F_{3}=tF_{1}+(1-t)F_{2},\ t\in \left[ 0,1\right] \) is univalent and convex in one direction.
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Communicated by Adrian Constantin.
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Mishra, O. Linear combination of convolution of harmonic univalent functions. Monatsh Math 203, 873–881 (2024). https://doi.org/10.1007/s00605-023-01842-1
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DOI: https://doi.org/10.1007/s00605-023-01842-1