Fixed point theorems and convergence theorems for Suzuki-generalized nonexpansive mappings in CAT(0) spaces

Let K be a nonempty subset of a metric space. A mapping T : K → K is said to satisfy condition (C) (sometimes called Suzuki-generalized nonexpansive) if 1 2 d ( x , T x ) ≤ d ( x , y ) implies d ( T x , T y ) ≤ d ( x , y ) for all  x , y ∈ K . In this paper, we obtain fixed point theorems and convergence theorems for such mappings in a CAT(0) space setting. Our results extend and improve many results in the literature.