Coefficient estimates and other properties for a class of spirallike functions associated with a differential operator (Q2015521)

Summary: For \(0\leq\eta<1\), \(0\leq\lambda<1\), \(-\pi/2<\gamma<\pi/2\), \(0\leq\beta\leq\alpha\), and \(m\in\mathbb N\cup\{0\}\), a new class \(S^m_{\alpha,\beta}(\eta,\gamma,\lambda)\) of analytic functions defined by means of the differential operator \(D^m_{\alpha,\beta}\) is introduced. Our main object is to provide sharp upper bounds for the Fekete-Szegő problem in \(S^m_{\alpha,\beta}(\eta,\gamma,\lambda)\). We also find sufficient conditions for a function to be in this class. Some interesting consequences of our results are pointed out.