Some properties of certain subclasses of harmonic univalent functions (Q345222)

Summary: For harmonic univalent functions of the form \(f(z)=z+\sum^\infty_{n=2}a_nz^n+\sum^\infty_{n=1}\overline{b}_n\overline{z}^n\), normalized with \(f(0)=f'_z(0)-1=0\), in the open unit disk \(U\), the author investigated the class \(H(\zeta_1,\zeta_2;\gamma)\) of \(f(z)\), obtain a characterization and its closure under convolution for some complex number \(\zeta_1,\zeta_2\) and some real number \(\gamma\). We also give a condition under which the integral operator of the form \(H(z)=\int^z_0\prod^k_{i=1}\bigg(\frac{f_i(s)}{s}\bigg)^{1/\alpha}ds\) is starlike.