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- W2967078975 abstract "We show that the convolution of the harmonic function $f=h+bar{g}$, where $h(z)+{e}^{-2{i}gamma}g(z)=z/(1-{e}^{{i}gamma}z)$ having analytic dilatation ${e}^{{i}theta} z^n (0leqtheta<2pi)$, with the mapping $f_{a,alpha}=h_{a,alpha}+overline{g}_{a,alpha}$, where $h_{a,alpha}(z)=(z/(1+a)-{e}^{{i}alpha}z^2/2)/(1-{e}^{{i}alpha}z)^2$, $g_{a,alpha}(z)=(a {e}^{2{i}alpha}z/(1+a)-{e}^{3{i}alpha}z^2/2)/(1-{e}^{{i}alpha}z)^2$ is convex in the direction $-(alpha+gamma)$. We also show that the convolution of $f_{a,alpha}$ with the right half-plane mapping having dilatation $(a-z^2)/(1-az^2)$ is convex in the direction $-alpha$. Finally, we introduce a family of univalent harmonic mappings and find out sufficient conditions for convexity along imaginary-axis of the linear combinations of harmonic functions of this family." @default.
- W2967078975 created "2019-08-22" @default.
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- W2967078975 creator A5085449137 @default.
- W2967078975 date "2017-03-10" @default.
- W2967078975 modified "2023-09-27" @default.
- W2967078975 title "Convexity in one direction of convolutions and linear combination of harmonic functions" @default.
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