Coefficient estimates for certain subclasses of analytic functions of complex order (Q653430)

The authors introduce and investigate the subclasses \(S_g(\lambda,\gamma)\) and \(K_g(\lambda,\gamma,m,u)\) (\(0\leq\lambda\leq 1\), \(u\in\mathbb{R}\setminus(-\infty,1]\), \(m\in \mathbb{N}\setminus\{1\}\)) of analytic functions of complex order \(\gamma\in\mathbb{C}\setminus\{0\}\), \(g: U\to\mathbb{C}\) being some suitably constrained convex function in the open unit disc \(U\). The authors obtain coefficient bounds and coefficient estimates involving the Taylor-Maclaurin coefficients of the function \(f(z)\) when \(f(z)\) is in the class \(S_g(\lambda,\gamma)\) or in the class \(K_g(\lambda,\gamma,m,u)\). The results presented in this paper generalize and improve those in related works of several authors.