Some Fixed-Point Results for the KF-Iteration Process in Hyperbolic Metric Spaces

Abstract

In this paper, we modify the KF-iteration process into hyperbolic metric spaces where the symmetry condition is satisfied and establish the weak w(2)-stability and data dependence results for contraction mappings. We also prove some D-convergence and strong convergence theorems for generalized (alpha,beta)-nonexpansive type 1 mappings. Finally, we offer a numerical example of generalized (alpha,beta)-nonexpansive type 1 mappings and show that the KF-iteration process is more effective than some other iterations. Our results generalize and improve several relevant results in the literature.