Fixed point approximation for $SKC$-mappings in hyperbolic spaces.

In this paper, we introduce the class of $SKC$-mappings, which is a generalization of the class of Suzuki-generalized nonexpansive mappings, and we prove the strong and Δ-convergence theorems of the S-iteration process which is generated by $SKC$-mappings (Karapinar and Tas in Comput. Math. Appl. 61:3370-3380, 2011) in uniformly convex hyperbolic spaces. As uniformly convex hyperbolic spaces contain Banach spaces as well as $\operatorname {CAT}(0)$ spaces, our results can be viewed as an extension and generalization of several well-known results in Banach spaces as well as $\operatorname {CAT}(0)$ spaces. [ABSTRACT FROM AUTHOR]