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

Let KK be a nonempty subset of a metric space. A mapping T:K→KT:K→K is said to satisfy condition (C) (sometimes called Suzuki-generalized nonexpansive) if 12d(x,Tx)≤d(x,y)impliesd(Tx,Ty)≤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.