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SCHWARZIAN DERIVATIVES OF CONVEX MAPPINGS
(SUOMALAINEN TIEDEAKATEMIA, 2011)
A simple proof is given for Nehari's theorem that an analytic function f which maps the unit disk onto a convex region has Schwarzian norm parallel to f parallel to <= 2. The inequality in sharper form leads to the conclusion ...
A note on convex conformal mappings
(2019)
We establish a new characterization for a conformal mapping of the unit disk D to be convex, and identify the mappings onto a half-plane or a parallel strip as extremals. We also show that, with these exceptions, the level ...
Weaker conditions for subdifferential calculus of convex functions
(Elsevier, 2016)
In this paper we establish new rules for the calculus of the subdifferential mapping of the sum of two convex functions. Our results are established under conditions which are at an intermediate level of generality among ...
Lipschitz Continuity of Convex Functions
(Springer, 2020)
We provide some necessary and sufficient conditions for a proper lower semicontinuous convex function, defined on a real Banach space, to be locally or globally Lipschitz continuous. Our criteria rely on the existence of ...
ON CONVEX COMBINATIONS OF CONVEX HARMONIC MAPPINGS
(2017)
The family F-lambda of orientation-preserving harmonic functions f = h + (g) over bar in the unit disc D (normalised in the standard way) satisfying h' (z) + g' (z) = 1/(1 + lambda z)(1 + (lambda) over barz), z is an element ...