A Novel Subclass of Harmonic Functions: Coefficient Bounds, Distortion Bounds, and Closure Properties

Abstract

In this paper, we introduce a new subclass of harmonic functions that significantly improves our understanding of these functions in geometric function theory. We provide a comprehensive analysis of this subclass by deriving several important properties, including coefficient bounds and decay bounds, which are necessary to evaluate the behavior and limitations of functions in this class. Additionally, we establish sufficient coefficient conditions for harmonic functions to belong to this class. Moreover, we rigorously show that this subclass is closed under both convex combinations and convolutions, meaning that any convex combination or convolution of functions in this class will also belong to the class. These results provide valuable insights into the stability and applicability of the subclass and provide a solid framework for further theoretical explorations and practical applications in complex analysis.

Keywords

• harmonic functions
• convolution
• coefficient bounds
• distortion bounds
• closure properties