Fixed Point Theory in Distance Spaces by William Kirk & Naseer Shahzad

Author:William Kirk & Naseer Shahzad
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Since , being the union of an ascending chain of convex sets, is convex, the closure of is also convex. It follows that

The fact that this intersection consists of a single point follows from the CN inequality (9.1). Specifically, if u, v ∈ C and u ≠ v and if m is the midpoint of the segment , then by (9.1)

This implies —a contradiction.

Definition 9.8.

Let be a complete CAT space. A bounded net in X is said to Δ-converge to z ∈ X if z is the unique asymptotic center of every subnet of

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