Abstract
We introduce the notion of local uniform linear convexity of bounded convex domains with respect to their Kobayashi distances.
Highlights
In [4] the author has proved that if B is an open unit ball in a Cartesian product l2 × l2 furnished with the lp-norm · and kB is the Kobayashi distance on B, the metric space (B, kB) is locally uniformly linearly convex. We introduce this kind of local uniform convexity in bounded convex domains in complex reflexive Banach spaces and we apply this notion in the fixed-point theory of holomorphic mappings
We recall several useful properties of the Kobayashi distance kD, which are common to all bounded and convex domains in reflexive Banach spaces
We study the structure of the fixed-point set of a holomorphic mapping
Summary
In [4] the author has proved that if B is an open unit ball in a Cartesian product l2 × l2 furnished with the lp-norm · and kB is the Kobayashi distance on B, the metric space (B, kB) is locally uniformly linearly convex.In this paper, we introduce this kind of local uniform convexity in bounded convex domains in complex reflexive Banach spaces and we apply this notion in the fixed-point theory of holomorphic mappings. 2. We introduce this kind of local uniform convexity in bounded convex domains in complex reflexive Banach spaces and we apply this notion in the fixed-point theory of holomorphic mappings.
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