Some fixed point theorems for an iteration method obtained by geometric approach

In recent years, many studies have been conducted to improve the performance of iteration methods. In this context, the new iteration methods developed by Kanwar et al. in 2021 are an important innovation in the literature. When it comes to iteration methods, one of the most important issues to consider is the convergence speed of these methods. In recent years, iteration methods that converge faster than the iteration methods obtained in previous years have been continuously proposed. Some iteration methods were developed by Sharma et al in 2024 and it was shown that these methods converged faster than the iteration method developed by Kanwar et al. These methods have shown faster convergence and applicability to a wider class of problems, not only theoretically but also in applied mathematics. In this thesis, an iteration method that converges faster than the iteration method developed by Sharma et al. The convergence speed of this new method is compared with the other iteration method and the stability and data dependency results are analyzed.