The Schwarz lemma stands as a cornerstone result in complex analysis, constraining holomorphic self-mappings of the unit disc by bounding both their magnitude and derivative. Traditionally, it affirms ...

In this paper we discuss holomorphic mappings f of the unit disc 𝕌 and corresponding index defined as I f ( z )= zf'( z ) f( z ) . We are interested in finding bounds on the growth of functions f and ...

This is a preview. Log in through your library . Abstract Let D be an annulus in the complex plane with closure D and boundary ∂ D. We prove that a function f, holomorphic in D with C1 + ε(∂ D) ...

Analytic functions, also known as holomorphic functions, form the cornerstone of complex analysis, widely studied for their elegant properties and deep connections in both pure and applied mathematics ...