Geometric Function Theory (GFT) originates from the celebrated Riemann mapping theorem of 1851. The first rigorous proof emerged in 1900. C. Carathéodory provided proof in 1912 using normal families and Riemann surfaces. P. Koebe gave proof that does not require Riemann surfaces. In 1916, L. Bieberbach conjectured a bound for the coefficients of the inverse of these mappings. This conjecture initiated the development of GFT.

Although this conjecture and several others were affirmatively settled, there are new conjectures and problems that attract the attention of researchers. GFT of harmonic mappings and of bi-complex and hyper-complex variables are actively pursued in research. In addition, there are numerous problems in the classical GFT to be solved. For example, we need to find the length of ray images, coefficient estimates for functions belonging to several subclasses of analytic starlike and convex mappings. Moreover, research discussing harmonic mapping analogues to the classical GFT results needs to be further explored. The theory of differential subordination for harmonic mapping is not yet fully exploited. Although there are some GFT applications in other fields, finding applications is also essential.

The aim of this Special Issue is to solicit original research and review articles focussing on the latest developments in this research area and the applications of GFT to other research areas. We hope that this Special Issue provides a platform for researchers in different areas of analysis and applied mathematics to come together and exchange ideas on how we can further apply GFT.

Potential topics include but are not limited to the following:

• Univalent and multivalent functions
• Harmonic univalent functions
• Quasiconformal mappings
• Bi-complex variable theory
• Hypercomplex functions
• Entire and meromorphic functions
• Value distribution theory
• Approximation theory
• Riemann surfaces
• Spaces of analytic and meromorphic functions
• Generalized function theory
• Universal functions
• Analysis of metric spaces