Strong convergence theorem for new four-step iterative method

In this paper, we introduce a new iterative method, namely the J-New iterative method. We prove its strong convergence result using a contractive condition. We also study the stability of the J-New iterative method. We present a comparison theorem showing that the J-New method converges faster than the J-Hammad method. Moreover, we give numerical examples to validate the performance of our algorithm and compare the rate of convergence of the J-New algorithm with the J-Hammad, J-Khan, J-SP, J-Noor, J-Ishikawa, and J-Mann algorithms. Specifically, we show that the convergence rate of the J-New method is superior to that of the other methods mentioned, establishing it as the most efficient among the compared iterative techniques. Also, we give an application of our main result.