Generalized Briot-Bouquet Differential Equation Based on New Differential Operator with Complex Connections

Abstract

A class of Briot–Bouquet differential equations is a magnificent part of investigating the geometric behaviors of analytic functions, using the subordination and superordination concepts. In this work, we aim to formulate a new differential operator with complex connections (coefficients) in the open unit disk and generalize a class of Briot–Bouquet differential equations (BBDEs). We study and generalize new classes of analytic functions based on the new differential operator. Consequently, we define a linear operator with applications.

Keywords

• differential operator
• univalent function
• analytic function
• subordination
• unit disk