How convex is a lens map?

Abstract

Abstract The crystalline lens of the human eye possesses a distinct convex shape, a subject that has garnered significant attention in optical research. In our study, we delve into the methodologies for quantifying the convexity of these lenses. Utilizing lens maps as our foundational model, we demonstrate that these mappings exhibit convexity of order β > 0 $\beta >0$ and are starlike of order α > 0 $\alpha >0$ . Furthermore, we establish a direct correlation between these orders and the opening angle of the lens map.

Keywords

• Convexity
• Lens maps
• Starlikeness