# Convergence rate of implicit iteration process and a data dependence result

## TL;DR

This paper introduces an implicit S-iteration process in W-hyperbolic spaces, demonstrating its faster convergence compared to other iterative methods and establishing a data dependence result for contractive mappings.

## Contribution

It presents a new implicit S-iteration process with proven superior convergence rate and a data dependence theorem in the context of W-hyperbolic spaces.

## Key findings

- Implicit S-iteration converges faster than Mann and Ishikawa iterations.
- Numerical example supports the theoretical convergence results.
- Data dependence result established for contractive mappings.

## Abstract

The aim of this paper is to introduce an implicit S-iteration process and study its convergence in the framework of W-hyperbolic spaces. We show that the implicit S-iteration process has higher rate of convergence than implicit Mann type iteration and implicit Ishikawa-type iteration processes. We present a numerical example to support the analytic result proved herein. Finally, we prove a data dependence result for a contractive type mapping using implicit S-iteration process.