On a result by Clunie and Sheil-Small
Dariusz Partyka, Ken-ichi Sakan (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
In 1984 J. Clunie and T. Sheil-Small proved ([2, Corollary 5.8]) that for any complex-valued and sense-preserving injective harmonic mapping in the unit disk , if is a convex domain, then the inequality holds for all distinct points . Here and are holomorphic mappings in determined by , up to a constant function. We extend this inequality by replacing the unit disk by an arbitrary nonempty domain in and improve it provided is additionally a quasiconformal mapping...