Schwarzian derivative and convexity of order α

Autor: Malik, Somya, Ravichandran, V.
Zdroj: The Journal of Analysis; March 2023, Vol. 31 Issue: 1 p201-228, 28p
Abstrakt: For 0⩽α<1, a normalised analytic function fdefined on the unit disc Dis convex of order αif ReQCV(f)>α, where QCV(f):=1+zf′′(z)/f′(z). We find numerous sufficient conditions for the function fto be a convex function of order αin terms of QCV(f)and QSD(f):=z2{f,z}, where {f,z}:=(f′′(z)/f′(z))′-(f′′(z)/f′(z))2/2is the Schwarzian derivative of f. We obtain these conditions by using the theory of second order differential subordination.
Databáze: Supplemental Index
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