On the Fixed Point Outcomes of a Modified Iteration Procedure on Kohlenbach Hyperbolic Space with an Application

We modify an iteration (repetition) process and prove the weak h- \(w^{2}\) -stability and data dependence theorems of this modified (altered) iteration process on Kohlenbach hyperbolic space (KHS) in this chapter. Furthermore, for two different forms of generalized non-expansive map (NM) on KHS, certain \(\triangle \) -convergence and strong convergence theorems utilizing the altered iteration process are proved. Finally, we show how our outcomes can be applied to non-linear integral equations. The outcomes obtained in this chapter are extensions, improvements, and generalizations of several known outcomes in fixed point (FP) theory literature.