New subclasses of certain analytic functions (Q717222)

For a normalized analytic function \(g\) on the open unit disk of the complex plane and certain real numbers \(\alpha\) and \(\delta\), the authors define \(\mathcal{P}(\alpha, \delta, g)\) to be the class of all normalized analytic functions \(f\) satisfying \(|f'(z)- \exp(i\alpha) (g(z)/z)| <\delta\). The class \(\mathcal{Q}(\alpha,\delta, g)\) consists of functions satisfying \(| (f(z)/z)- \exp(i\alpha) g'(z)| <\delta\). The authors obtain necessary and sufficient conditions for functions to belong to the above classes. Also, certain related results are obtained.