(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
In this manuscript, we study the split null point problem in the settings of real Hilbert spaces using two different iterative methods. In our first method, we propose a self-adaptive algorithm with an inertial technique for solving split common null point problem and fixed point of a finite family of a demimetric mapping without the computation of the resolvent of a monotone operator. In our second method, we propose a self-adaptive algorithm with a multi-step inertial technique to approximate a solution of the aforementioned problems and to accelerate the rate of convergence of our iterative method. The selection of the stepsize employed in our iterative algorithms does not require prior knowledge of the operator norm. Lastly, we present a numerical example to show the performance of our iterative algorithms. The result discussed in this article extends and complements many related results in literature.