Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality

Abstract

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given.

Keywords

• harmonic function
• convolution
• coefficient estimates
• graphics