Let ( X, d ) be a complete uniformly convex hyperbolic space.
Let be a complete uniformly convex metric space with a monotone modulus of convexity.
Let ((X,d)) be a complete uniformly convex metric space with monotone modulus of uniform convexity.
Let be a complete uniformly convex hyperbolic space with monotone modulus of uniformconvexityη.
Let ((X, d, W)) be a complete uniformly convex hyperbolic space with monotone modulus of uniform convexity η.
Let be a complete uniformly convex metric space with a monotone modulus of convexity and a bounded sequence in.
In the sequel, we always assume that ((X,d, W)) is a complete uniformly convex hyperbolic space with a monotone modulus of uniform convexity η and K is a nonempty closed subset of X, and (T: Kto P K)) is an SKC-type multi-valued mapping.
Denote begin{aligned} W( x, y, alpha) = & alpha x + ( 1- alpha) y,quad text{for all } x, y in C, end{aligned} (4.1) then ((X, d,W)) is a complete uniformly convex hyperbolic space with a monotone modulus of uniform convexity and C is a nonempty closed and convex subset of X.
Denote by W x,y,alpha):= alpha x + 1-alpha yy, quad forall x, y in X mbox{ and } alphain[0, 1-alpha y((X, d, W)) is a complete uniformly convex hyperbolic space with a monotone modulus of uniform convexity and K is a nonempty closed and convex subset of X.
Notice that (see [32], Lemma 1.10) given a bounded sequence ({x_{n}} subset X), where X is a complete uniformly convex hyperbolic space with a monotone modulus of uniform convexity η, such that Δ- lim_{n} x_{n} = x) and for any (y in X) we have (y neq x), then lim_{n toinfty} d( x_{n}, x) < lim_{n toinfty} d( y_{n}, y).
Theorem 3.3 Let X be a complete geodesic Ptolemy space with a uniformly continuous midpoint map.
