The Department of Mathematics at the College of Science, University of Baghdad, recently hosted an academic lecture titled ” The Theory of Geometric Functions and its Fundamental Concepts.”
This lecture provided a comprehensive exploration of the core principles of geometric function theory, with particular emphasis on the critical concepts of subordination and dominance, which play significant roles in analysing univalent functions, fractional calculus, and differential equations.
These concepts apply to many fields, such as in mathematics, engineering, and the physical sciences, making them highly relevant in real-world scenarios.
In engineering, for example, the theory of geometric functions is used to design efficient signal-processing algorithms. Furthermore, the lecture highlighted the importance of geometric function theory as a fundamental discipline in complex analysis, emphasising the geometric characteristics of analytic functions.
The theory was also discussed from a practical perspective, particularly in fields such as image and signal processing. The lecture addressed the concept of bounded rotation functions. Derivatives from these possess positive fundamental components. The intricate connections between the functions were explained, including various types of univalent analytic functions and their generalisations within complex analysis.