Convex mappings on the unit ball ofC n

Unbounded convex mappings of the ball in $\mathbb {C}^n$

“…Example 2.3. From a result in [2] (Corollary 1), if f is a univalent analytic mapping of the unit disk in the plane onto a convex domain, then the mapping…”

The Generalized Roper-Suffridge Extension Operator on the Reinhardt Domain

“…The first was proved by Roper and Suffridge when they introduced their operator [19], while the second result was given by Graham and Kohr [5]. Until now, it is difficult to construct the concrete convex mappings, starlike mappings on n B .…”

On the generalized Roper‐Suffridge extension operator in Banach spaces

“…In [11], Roper and Suffridge introduced an extension operator, which is defined for normalized locally univalent function f on U by…”

“…This operator is known as the Roper-Suffridge extension operator. Roper and Suffridge [11] proved that if f is a normalized convex function on U, then Φ n ( f ) is a normalized biholomorphic convex mapping on B n . In [7], Graham and Kohr proved that (1) if f is a normalized starlike function on U, then Φ n ( f ) is a normalized biholomorphic starlike mapping on B n ; (2) if f is a normalized Bloch function on U, then Φ n ( f ) is a normalized Bloch mapping on B n .…”