Comprehensive family of uniformly analytic functions

Abstract

We introduce the subclass $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ of analytic functions with negative coefficients. Coefficient inequalities, distortion theorems, closure theorems, radii of close-to-convexity, starlikeness, and convexity for functions belonging to the class $ \mathcal{U}_{\mathcal{T}}(\Phi ,\Psi ;\alpha ,\beta ) $ are obtained. We also determine integral operators for functions in this class and some properties involving modified Hadamard products of several functions belonging to the class $ \mathcal{U}_{\mathcal{T}}^*(\Phi ,\Psi ;\alpha ,\beta ) $.