Combinations of geometric expressions implying schlichtness.

Abstract

In this short paper we prove an interesting result that certain not-linear combinations of geometric expressions of the form φ(f,f^',f^'' )+λϕ(f,f^',f^'') imply schlichtness of holomorphic functions, normalized by f(0) and f^' (0)=1, in the unit disk E={z∈ C:|z|<1}