Given two functionsf(z),g(z) in the (usual) classS, we can form the new functions (arithmetric and geometric mean functions) F(itz)=∝(itf)(itz)+β(itg)(itz) and G(itz)=(itz)(f(itz)/(itz))(su∝)(g(itz)/(itz))(suβ), whereα, β ∈ (0, 1) andα+β=1. This paper determines the maximum valence of the functionsF andG.
Unit Circle Unit Disk Negative Integer General Means Large Disk
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