A subclass of harmonic functions related to a convolution operator (Q324649)

A harmonic function \(f(z) = h(z) + \overline{g(z)} \) in the unit disc \(\mathbb D\) is in the class \(\mathcal S_{\mathcal H}\) if it is univalent and sense-preserving. Furthermore, the function \(f\) is said to be star-like of order \(\beta, \, 0\leq \beta<1\), if NEWLINE\[NEWLINE \text{Re }\left(\frac{zh^\prime(z) - \overline{z g^\prime(z)}}{h(z) + g(z)} \right) >\beta. NEWLINE\]NEWLINE This class was studied by \textit{J. M. Jahangiri} [J. Math. Anal. Appl. 235, No. 2, 470--477, Art. No. jmaa.1999.6377 (1999; Zbl 0940.30003)]. In the present paper the authors introduce some new subclasses of \(\mathcal S_{\mathcal H}\) using the generalized hypergeometric function. The authors derive coefficient bounds, extreme points, and prove inclusion results for these classes. They also show that these classes are closed under the generalized Bernardi-Livingston integral operator.